How many permutations

Q: How many different passwords of 4 characters can be made using the numbers from 0 to 9 and the…

A: A password of four characters is to be made using the numbers from 0 to 9 i.e. 10 digits and the…

Q: Find the number of the permutation of 8 different things taken 3 at a time

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Q: A number N is divisible by 4 iff the number formed by the last 2 digits of N is divisible by 4. For…

A: We can find number divisible by 4  by using the concept given in the question

Q: How many natural numbers that are less or equal to 1000 and that are not multiples of 3, 5, or 7…

A: A number is said to be divisible by other number if on dividing the number  with it given remainder…

Q: How many different three digit numbers can be made from the set of integers {1,2,3,4,5,6,7,8,9} if…

A: The set of integers {1,2,3,4,5,6,7,8,9}

Q: How many ways can a DVD collection of 12 different movies be arranged in alphabetical order on a…

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Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, and 9, which are divisible by 5,…

A: Given information- We have given the digits- 2, 3, 5, 6, and 9. We have to form the 3 digits numbers…

Q: Assume that you select digits from the set {1,2,3,4,5,7,8} to form a number between 10 and 800. (1)…

A: given set of digits is  {1,2,3,4,5,7,8}  and the range of numbers is 10 to 800. There would be 2…

Q: Use any method, list all the three digit numbers from the set {3,4,5,6} where there are no repeating…

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Q: How many different 3 letter codes can I make that do not contain any repeated letters

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Q: How many permutations of the numbers (1, 2, 3, 4, 5, 6, 7, 8, 9} have the numbers 4, 5 and 6 in…

A: So, the numbers 4, 5 & 6 should remain at their natural position and the other numbers can…

Q: How many integers between 1 and 822 inclusive are divisible by 5 or 3?

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Q: Question * How many three-digit numbers can be made from the digits 0,1, 2, 3 and 4, used at most…

A: In the modern era of technology and digitization, the field of data science has become increasingly…

Q: Suppose we want to form four-digit numbers using the set of digits {0,1, 6, 7, 9}. For example, 9071…

A: The first number can be selected in 4 ways. [ Any number from {1,6,7,9} ] The second number can be…

Q: How many numbers between 1234 and 1234567 are of 5? multiples of 2 or multples

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Q: Q15. What is the first (rightmost) digit in the base 3 expansion of the base 10 number71?

A: Given: 15. A base 10 number 71. To find: The first(rightmost) digit in the base 3 expansion of given…

Q: How many odd integers from 1,000 through 9,999 have distinct digits?

A: From 1000 to 9999 , all are 4 digited integers.  If the integer is odd then the last digit can occur…

Q: How many different numbers with nonrepeating digits from 4000 to 6000 can be produced using the…

A: The problem can be solved using the concept of permutation and combination.

Q: How many 5- digit numbers can be formed using the digits 0,1,2,3,4,5,6,7,8,9, if repetitions of…

A: Givendigits = 0,1,2,3,4,5,6,7,8,9No.of digits =10

Q: How many integers between 100 and 999 inclusive are multiples of 13?

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Q: How many 4 digit numbers can be formed using only the numbers 3 2 7 6 0 4 9 if the number is odd and…

A: numbers: {3,2,7,6,0,4,9} make 4 digit numbers  no repeatation odd numbers: last digit must be odd.…

Q: How many ways to arrange 7 books on the shelf exist if two definite books are not placed together?

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Q: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

A: How many distinct four-digit integers can one make from the digits 1,3,3,7,7, and 8?

Q: How many different three digit numbers can be formed using the digits 8,1,5, and 7 with repetition ?…

A: To determine: The different three digit numbers can be formed using the digits 8, 1, 5, and 7 with…

Q: How many six-digit even numbers more than 200,000 can be formed using all of the digits 1, 1, 2, 2,…

A: Step 1: Step 2: Step 3: Step 4:

Q: How many ways are there to rearrange the letters in the 12 letter string "AAAAABBBBCCD"? Enter your…

A: given data,n=12 letters letters :A :5  B : 4 C :2 D :1 we have to find out the no. of ways to…

Q: how many 3-digit number we can form using 10 digits (0,1,2,3.......,8) if no repetition is allowed

A: The first digit have 9 choices (digits 1 -9) as zero cannot be the first digit.There will be 9…

Q: How many integers between 10000 and 1000000 have no digits other than 5, 7 or 9. How many have no…

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Q: Let ß = (1,3,5,7,9,8,6)(2,4,10). What is the smallest positive integern for which ßn = ß-5?

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Q: How many numbers can be made each using all the numerals in the set S = {1,2,2,3, 3, 3, 0}

A: According to the provided information, The set are S= {1, 2, 2, 3, 3, 3, 0}

Q: How many 3-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 0, which are divisible by 5…

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Q: How many four digit codes can be made out of the digits 0,2,4and 8 if the repetition of digits is…

A: We have to find four digit codes can be made out of the digits 0,2,4and 8 ....

Q: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

A: How many 4-digit numbers greater than 5000 can be formed from the digits 2, 4, 5, 7, 8, and 0?…

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.