How many solutions are there to the equation X1+X2+X3+X4 = 10 where X1, X2, X3 and X 4 are nonnegative integers such that X1≥2, X2≥3?

• 56

• 252

• 84

• 5

• 112

How many different strings can be made from the letters in STATISTICS, using all the letters?

• 10!

• 720

• 50400

• 100800

• C(10,3)

Find the coefficient of x^4 y^2 in (3x-5y)^6 .

• 3*(5^3)

• (3^4)*(5^2)

• (3^5)*(5^3)

• 15

• -15

Find the coefficient of x^7 y^5 in (x + y)^12

• 664

• 792

• 21

• 72

• 99

Fifty tickets, numbered 1, 2, 3, …, 50, are sold to 50 different people for a drawing. Six different prizes are awarded, including a grand prize (a trip to Moscow). How many ways are there to award the prizes if the person holding ticket 13 wins the grand prize?

• P(50, 5)

• C(50, 6)

• P(49, 5)

• C(49, 5)

• P(49, 6)

Let A = {a, b, c, d, e, f}. How many 4-combinations of A are there?

• 360

• 60

• 30

• 15

• 120

Let S = {1, 2, 3, 4, 5}. How many 3-permutations of S are there?

• 120

• 60

• 10

• 24

• 4

How many permutations of {1, 2, 3, 4, 5} end with 3?

• 120

• 12

• 4

• 24

• 6

Find a decreasing subsequence of maximal length in the sequence 13, 14, 7, 6, 15, 22, 10, 4, 25, 1.

• 13, 14, 15, 22, 25

• 25, 22, 15, 14, 13, 10, 7, 6, 4, 1

• 22, 10, 4, 1

• 14, 7, 6, 4, 1

• 6, 15, 22, 25

How many bit strings are there of length four or less?

• 16

• 8

• 4

• 31

• 32