Note: In this problem set, the notation C(n, k) is used for the combination "n choose k." Alternate notation: ( ) 3.) Five cards are marked with the numbers 1, 2, 3, 4, 5, then shuffled, and 2 cards are drawn. (a) How many different 2-card combinations are possible? (b) How many 2-card hands contain a number less than 3?

Decide whether the exercise involves permutations or​ combinations, and then solve the problem.   In a club with 11 male and 10 female​ members, how many 5​-member committees can be chosen that have   ​(a) at least 4 ​women? ​(b) no more than 2 ​men? Does the problem involve permutations or​ combinations? ​(a) There can be nothing 5​-member committees with at least 4 women.

Simplify each binomial coefficient or permutations to factorial fractions: () - n! n! P(n, k) = (n – k)!k! (n – k)! You need not simplify these expressions, such as 15ª or 17!, in your response. Photos and Money Lee wants to hang 8 of his 20 photos in an ordered line on the wall above his desk. How many ways can he do this? Lee wants to select 9 photos of his 20 to take on a trip. How many ways can he do this? Lee has decided to give his collection of 20 unique photographs to his three children. In how many ways can he partition his photo collection among this three children where it may be that some children get no photographs? Lee also has 500 dollars he wants to give his three children. In how many ways can he divide it among his three children? It may be the case that a child receives no money. Lee's children will be upset if he doesn't give each of them at least 50 dollars. How many ways can Lee partition his money so his children won't be upset?

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