Suppose that 18 red beads, 12 yellow beads, eight blue

Three pollsters will canvas a neighborhood with 21 houses. Each pollster will visit seven of the houses. How many different assignments of pollsters to houses are possible?

Suppose that 18 red beads, 12 yellow beads, eight blue beads, and 12 black beads are to be strung in a row. How many different arrangements of the colors can be formed?

Suppose that two committees are to be formed in an organization that has 300 members. If one committee is to have five members and the other committee is to have eight members, in how many different ways can these committees be selected?

If the letters s, s, s, t, t, t, i, i, a, c are arranged in a random order, what is t

Suppose that n balanced dice are rolled. Determine the probability that the number j will appear exactly nj times (j = 1,..., 6), where n1 + n2 + ... + n6 = n.

If seven balanced dice are rolled, what is the probability that each of the six different numbers will appear at least once?

Suppose that a deck of 25 cards contains 12 red cards. Suppose also that the 25 cards are distributed in a random manner to three players A, B, and C in such a way that player A receives 10 cards, player B receives eight cards, and player C receives seven cards. Determine the probability that player A will receive six red cards, player B will receive two red cards, and player C will receive four red cards.

A deck of 52 cards contains 12 picture cards. If the 52 cards are distributed in a random manner among four players in such a way that each player receives 13 cards, what is the probability that each player will receive three picture cards?

Suppose that a deck of 52 cards contains 13 red cards, 13 yellow cards, 13 blue cards, and 13 green cards. If the 52 cards are distributed in a random manner among four players in such a way that each player receives 13 cards, what is the probability that each player will receive 13 cards of the same color?

Suppose that two boys named Davis, three boys named Jones, and four boys named Smith are seated at random in a row containing nine seats. What is the probability that the Davis boys will occupy the first two seats in the row, the Jones boys will occupy the next three seats, and the Smith boys will occupy the last four seats?

Prove the multinomial theorem 1.9.1. (You may wish to use the same hint as in Exercise 20 in Sec. 1.8.)

Return to Example 1.8.6. Let S be the larger sample space (first method of choosing) and let S be the smaller sample space (second method). For each element s of S , let N (s )stand for the number of elements of S that lead to the same boxful s when the order of choosing is ignored. a. For each s S , find a formula for N (s ). Hint: Let ni stand for the number of items of type i in s for i = 1,..., 7. b. Verify that  s S N (s ) equals the number of outcomes in S.