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Chapter 1: Q. 1.2 (page 15)

How many outcome sequences are possible when a die is rolled four times, where we say, for instance, that the outcome is 3, 4, 3, 1 if the first roll landed on 3, the second on 4, the third on 3, and the fourth on 1?

Short Answer

Expert verified

The number of possible sequences are6×6×6×6=64

Step by step solution

01

  Step 1 .Given information

Here a die is rolled four times, we have to find out the possible number of sequences of out comes

02

.  Finding the  number of possible sequences of outcomes

If a die is rolled for on time, the outcomes are 1,2,3,4,5,6, that is 6 outcomes. Then the die is rolled four times, the outcomes are repeated four timesrole="math" localid="1647497151106" thatis6×6×6×6=64times

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Most popular questions from this chapter

An elevator starts at the basement with 8people (not including the elevator operator) and discharges them all by the time it reaches the top floor, number6. In how many ways could the operator have perceived the people leaving the elevator if all people look alike to him? What if the 8people consisted of 5men and 3women and the operator could tell a man from a woman?

How many subsets of size 4of the set localid="1649163905451" role="math" S=1,2,...,20contain at least one of the elements 1,2,3,4,5?

How many different 7-place license plates are possible when 3of the entries are letters and 4 are digits? Assume that repetition of letters and numbers is allowed and that there is no restriction on where the letters or numbers can be placed.

From a set of npeople, a committee of size jis to be chosen, and from this committee, a subcommittee of size i, i≤j, is also to be chosen.

(a) Derive a combinatorial identity by computing, in two ways, the number of possible choices of the committee and subcommittee—first by supposing that the committee is chosen first and then the subcommittee is chosen, and second

by supposing that the subcommittee is chosen first and then the remaining members of the committee are chosen.

(b) Use part (a) to prove the following combinatorial identity:role="math" localid="1648189818817" ∑j=innjji=ni2n-i;i≤n

(c) Use part (a) and Theoretical Exercise 13 to show that:role="math" localid="1648189841030" ∑j=innjji-1n-j=0;i<n

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