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Chapter 13: Q. 38 (page 855)

Forming Codes How many different four-letter codes are there if only the letters A, B, C, D, E,andF can be used and no letter can be used more than once?

Short Answer

Expert verified

There are 360 ways to write a four-letter code.

Step by step solution

01

Step 1. Given information. 

Four-letter code is to be formed using the letter A, B, C, D, E, and F.

Repeated letters are not allowed.

02

Step 2. Determine the possible number of codes. 

We are choosing 4 letters from 6 letters and arranging them in order. In the ordered arrangement a letter cannot be repeated.

This is an example of a permutation without repetition in which 4 objects are chosen from 6 distinct objects.

P(6,4)=6!(6-4)!=6!2!=6路5路4路3路2!2!=360

03

Step 3. Conclusion.

There are 360 ways to write a four-letter code.

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Most popular questions from this chapter

Find the probability of the indicated event if P(A)=0.25andP(B)=0.45

P(A鈭�B)ifP(A鈭�B)=0.6

List all the combinations of 6 objects 1, 2, 3, 4, 5, and 6 taken 3 at a time. What is C(6,3)?

An urn contains 15 red balls and 10 white balls. Five balls are selected. In how many ways can the 5 balls be drawn from the total of 25 balls:
(a) If all 5 balls are red?

(b) If 3 balls are red and 2 are white?

(c) If at least 4 are red balls?

Use the formula C(n,r)=n!(n-r)!r!to find the value of each combination.

C(26,13)

In a probability model, which of the following numbers could be the probability of an outcome?

00.010.35-0.411.4
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