Define Permutation and Combination in your own wo

Q: lease explain in simple steps how you calculate the last two digits of 21000 in modular arithmetic…

A:

Q: 15!/14! *

A:

Q: I am looking for if

A: To find x from the given equation

Q: 195!/192!

A: Factorial means multiplying all the integers till the number.  n!= 1×2×3×......×n   We can rewrite…

Q: low many different sequences of 4 digits are possible if the first digit must be 3, 4, or 5 and if…

A: To find the number of different sequences of 4 digits following the given conditions, we can…

Q: How many 3 digit even numbers can be created if repetition of digits is allowed

A:

Q: How many ways can you get we get a 2 digit passcode if zeros are not allowed?

A: If zero is not allowed, The number of available digits is 9 (1,2,3,4,5,6,7,8,9)

Q: Earlier this year, 240 caribou were caught and tagged. In a recent survey, 60 out of 350 caribou…

A: GivenThe total number of caribou tagged (population) =240The number of caribou caught this year…

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: Show that if 5000 boys registered for driving license during the last month(31 days) at driving…

A: Given that 5000 boys registered for driving license during the last month in 31 days at driving…

Q: Be able to demonstrate the fact that at least 10 of the 64 days selected must occur on the same…

A: let we have selected 64 daysThen day 1 is any one week day from 7weekdaysLet day 1 is weekday xAfter…

Q: A four-bit code word is any sequence of four digits, where each digit is either a 0 or a 1. For…

A: Here we have to form A Four bit code word of four digits using the digit 0 and 1

Q: How many natural numbers are there with a maximum of 7 digits, the sum of which is 31?

A: As per the question we have to find the total number of natural numbers between 0 to 9999999 whose…

Q: A passcode is to be created from 2 letters, 2 digits, and 2 special characters (consisting of ?, !,…

A: There are totally 26 alphabets, the first letter has 26 choices. Since there is no repetition of…

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

A:

Q: Show that 3+ V5 is irational number

A:

Q: give examples to show “classification” and “seriation” are pre number concepts.

A: Here, we will understand the concepts one by one with examples, See in step2 for details answer,

Q: Assume that you select digits from the set {2,3,5,7} to form a number between 20 and 700. (1) How…

A: The given set of digits is 2,3,5,7 and the range of numbers is 20 to 700. There would be 2 digit…

Q: suppose repetitions are not allowed. Find the number n of three-digit even nimbers that can be…

A: Given problem Given that   Suppose repetitions are not allowed. Given six digits : 2,3,5,6,7,9…

Q: Which of your birthdays, until your one hundredth, fall on the same day of the week as the day you…

A:

Q: How many different sequences of 5 ternary digits (0, 1, 2) are possible? The number of different…

A: There are total 3 choices for each digit. We will have to pick 5 digits. Each digit can be picked in…

Q: Is there any derivation of the formula of permutation and combination?

A: Derivation for the formula of permutation and combination . Permutation : (Arrangement of r things…

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: Certain automobile license plates consist of a sequence of three letters followed by four digits. If…

A: We have a license plate that consists of a sequence of three letters followed by four digits. The…

Q: Is the set O of all odd counting numbers (1, 3, 5… ) closed for multiplication? Why or why not?

A:

Q: A classic counting problem is to determine the number of different ways that the letters of…

A: The number of different ways to arrange a word:Consider the total number of letters in a word be…

Q: How many five​-digit numbers can be formed with the first two digits odd and the last three digits…

A: The number of digits need to be formed is five. The first two digits are odd and the last three…

Q: Show that the weighted arithmetic mean of first 'n' natural numbers whose weight are equal to the…

A:

Q: how many four-digit even numbers are possible if the leftmost digit cannot be zero? repitition is…

A: The question is to find how many 4 digits even numbers are possible if the left most digit cannot be…

Q: user passwords for a certain computer network consist of 6 letters( upper case ) followed by 4…

A: user passwords for a certain computer network consist of 6 letters( upper case ) followed by 4…

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: hy is the basic counting rule (BCR) often referred to as the multiplication rule?

A: Basic Counting Rule (BCR):If k actions can be done in a definite order with m1 possibilities for…

Q: How many different 3-digit numbers are possible using only the digits 1,5,6,7,8 ? How many…

A: We have to find no of ways for make 3 and 4 digit numbers  when repetition allow and not allowed

Q: What are the ten branches in mathematics?

A: Ten branches of mathematics are:-