Discrete Mathematics Answers

Let S be a finite nonempty set. Show that the number of subsets of S of even cardinality equals the number of subsets of S of odd cardinality.

Find the coefficient of x^7 y^9 in the expansion of (4x+ 5y)^16.

Find the number of terms in the complete expansion of (x+y)^150 after like terms are collected together.

12) Suppose that a room contains 10 cats and 15 dogs. How many ways are there to form a committee consisting of 6 of these animals if it must have more dogs than cats?

1) Suppose a group contains 7 men and 7 women. How many ways are there to arrange these people in a row if the men and women alternate?

Let S be a finite set, with |S|= 200. Find the number of subsets of S containing more than 2 elements

Compute the number of bit strings of length 14 that contain...
(a) exactly four 1s
(b) at most four 1s
(c) at least four 1s
(d) an equal number of 0s and 1s.

8) How many different 6-permutations are there of elements in the set {a, b, c, d, e, f, g, h}?

Assume that a class consists only of students residing the 50 US states. Find the smallest number of students that must be enrolled in a class to guarantee that there are at least 5 students from the same state

Let d be a positive integer. Show that among any group of d+ 1 (not necessarily consecutive) integers there are two with exactly the same remainder when they are divided by d.