Chapter 1: Q. 1.6 (page 19)

How many different $7$ -place license plates are possible when $3$ of 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.

Short Answer

Expert verified

The possible no. of license plates are $35 \times {(26)}^{3} \times {(10)}^{4}$ .

Step by step solution

Step 1. Given information.

Total no. of letters and digits on a license plate $= 7$

No. of letters on a license plate $= 3$

No. of digits on a license plate $= 4$

Digits and letters can be repeated and can be placed at any place.

Step 2. Find the possible no. of license plates.

No. of ways of selecting $3$ letters out of $7$ places $= \frac{7!}{3! 4!} = \frac{7 \times 6 \times 5 \times 4!}{3 \times 2 \times 1 \times 4!} = 35$

Out of localid="1648802616846" $26$ letters, localid="1648802620207" $3$ letters can be selected (with repetition) in $26! \times 26! \times 26! ways = {(26)}^{3}$

Out of localid="1648802623922" $10$ digits, localid="1648802627798" $4$ digits can be selected (with repetition) in $= 10! \times 10! \times 10! \times 10! ways = {(10)}^{4}$

Therefore, the possible no. of license plates are $35 \times {(26)}^{3} \times {(10)}^{4}$ .

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How many different $7$ -place license plates are possible when $3$ of 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.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the possible no. of license plates.

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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.

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Find the possible no. of license plates.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Pure Maths

Theoretical and Mathematical Physics

Decision Maths

Probability and Statistics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

How many different $7$ -place license plates are possible when $3$ of 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.