3. Given 20 people, how many ways are there to form a committee containing at le

Question

3. Given 20 people, how many ways are there to form a committee containing at least 3 people?

17.Find the number of 4-lists of the form(x1,x2,x3,x4), where each xi is a nonnegative integer and x1 + x2 + x3 + x4 = 15

1. Jeopardy! The following are answers to counting questions. Your job is to write a question for each.

a) nk - (n)k

b) nn - n!

c) 2n - 2

d) 35 -25

5.How many eight-character passwords are there if each character is either an uppercase letter A-Z, a lowercase letter a-z, or a digit 0-9, and where at least one character of each of the 3 types are used?

7. How many k-multisets taken from [n] are not also (ordinary) subsets of [n]?

9. How many nonempty subsets of [10] have the product of their elements even?

11. How many 5-letter worlds (uppercase letters only) do not both begin and end with a vowel?

15. You write down all of the integers from 1 to 1,000,000. How many times did you write the digit 4?

19. How many zeros does n! end with? Prove your answer.

Explanation / Answer

YOU POSTED MANY QUESTIONS , EACH NEEDING LARGE ARITHMETIC ..

POSTING RESPONSE TO FEW IN THIS ..SHALL POST RESPONSES FOR OTHERS IN SEPEARATE POSTS.

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