How many 3 digit number can be made using the five digits 3, 6, 7, 8, 9 when (a) repetitions are not allowed, and (b) repetitions are allowed? Answers:        a) 60 three-digit numbers can be formed.        b) 125 three-digit numbers can be formed

Q: Standard automobile license plates in a country display 2 numbers, followed by 3 letters, followed…

A: we know thatno.of letters (A to Z)=26no.of digits(0 to 1)=10

Q: The seven given numbers are: 5, 6, 3, 4, 1, 2, and 7. A. How many five-digit numbers can be formed…

A: Given seven numbers are5,6,3,4,1,2,7

Q: How many integers from 1 through 1000 are multiples of 7 or multiples of 4?

A: Let A be the set of integers that are multiples of 7 and B be the set of integers that are multiples…

Q: Using the digitd 3, 4, 5, 6, 7, 8, and 9, how many 4-digit numbers can be constructed if the number…

A: Solution: From the given information, the digits are 3, 4, 5, 6, 7, 8 and 9. Here, the numbers with…

Q: a) Evaluate: 21-12 + (4-10)

A: Given 21 - 12 ÷ ( 4 - 10 )

Q: In how many different ways can 12 people occupy the 12 seats in a front row of a mini theater ?

A: Given: The number of seats available is 12.  The number of people to be arranged in seats is 12.

Q: In choosing what music to play at a charity fund raising event Cory needs to have an equal number of…

A: If an event can be done in n different ways and an other event can be done in m different ways, then…

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

A:

Q: In how many different ways can ten books be arranged on a shelf?

A: Given that there are ten books available to arrange them in shelf.

Q: License plates in a certain state start with 3 letters (but they don’t use I or W) and then 3…

A:

Q: 23 Find the number of permutations of all the letters of the word NOTEPAD if: a) the letters can be…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: Let ab be a two-digit number. Now, swap its digits to form another two-digit number, multiply it by…

A: ab is a 2-digit number where, ab = 10a+b  When the digits of ab are swapped, we get the 2-digit…

Q: Using the digits 2, 3, 6, 8, and 9, how many 3-digit whole numbers can be formed if repetitions are…

A: Provided information is; if repetitions are not permitted we have to find how many 3-digit whole…

Q: In how many ways can we make combinations of three letters C, O, Y taken 1,2,3 at a time?(Answer in…

A: As you know combination is combining the group of items into one. While combining the items, the…

Q: How many 2-digit numbers of 2 different digits can be formed from the numbers 0,2,4,6,8? Select one:…

A:

Q: In how many different ways can 7 potted plants be arranged in a row with 5 spaces? O 720 O 2 520 5…

A: There are total 7 potted plantsThere are 5 spaces in a rowNumber of ways  to arrange 7 potted plants…

Q: In how many different ways can 4 passengers be seated in an airplane if each passenger can select…

A:

Q: license plates in a particular state display 2 letters followed by 3 numbers. how many different…

A:

Q: In how many ways can a teacher arrange 6 students in the front row of a classroom with a total of 20…

A:

Q: A license plate is to consist of 3 digits followed by 5 uppercase letters. Determine the number of…

A:

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.