Chapter 3: 5 (page 168)

Compute the number of ways can select n element from N element of each of the following:
$n = 2, N = 5$
$n = 3, N = 6$
$n = 5, N = 20$

Short Answer

Expert verified

10
20
15504

Step by step solution

Computing the number of ways to select 2 from 5

The value of ${}^{5}{C_{2}}$ can be computed using the formula mentioned below:

Here, $N = 5$ and $n = 2$ .

$(\frac{N}{N}) = \frac{N!}{n! (N - n)!} (\frac{5}{2}) = \frac{5!}{2! (5 - 2)!} = \frac{5 \times 4 \times 3 \times 2 \times 1}{(2 \times 1) \times (3 \times 2 \times 1)} = \frac{5 \times 4}{2 \times 1} = 10$

Therefore, the value of the number of ways to select2 from 5 using combination is 10.

Computing the number of ways to select 3 from 6

The value of ${}^{6}{C_{3}}$ can be computed using the formula where $N = 6$ and $n = 3$ .

$(\frac{N}{N}) = \frac{N!}{n! (N - n)!} (\frac{6}{3}) = \frac{6!}{3! (6 - 3)!} = \frac{6 \times 5 \times 4 \times 3 \times 2 \times 1}{(3 \times 2 \times 1) \times (3 \times 2 \times 1)} = \frac{6 \times 5 \times 4}{3 \times 2 \times 1} = 20$

Therefore, the value of ${}^{6}{C_{3}} = 20$ .

Computing the number of ways to select 5 from 20

The value of ${}^{20}{C_{5}}$ can be computed using the formula where $N = 20$ and $n = 5$ .

$(\frac{N}{N}) = \frac{N!}{n! (N - n)!} (\frac{20}{5}) = \frac{20!}{5! (20 - 5)!} = \frac{20 \times 19 \times 18 \times 17 \times 16 \times 15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1}{(5 \times 4 \times 3 \times 2 \times 1) \times (15 \times 14 \times 13 \times 12 \times 11 \times 10 \times 9 \times 8 \times 7 \times 6 \times 5 \times 4 \times 3 \times 2 \times 1)} = \frac{20 \times 19 \times 18 \times 17 \times 16}{(5 \times 4 \times 3 \times 2 \times 1)} = 15, 504$

Hence, the value of ${}^{20}{C_{5}} = 15504$ .

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Performance Measure	Number of Museums
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Compute the number of ways can select n element from N element of each of the following:
$n = 2, N = 5$
$n = 3, N = 6$
$n = 5, N = 20$

Short Answer

Step by step solution

Computing the number of ways to select 2 from 5

Computing the number of ways to select 3 from 6

Computing the number of ways to select 5 from 20

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Compute the number of ways can select n element from N element of each of the following:n=2,N=5n=3,N=6n=5,N=20

Short Answer

Step by step solution

Computing the number of ways to select 2 from 5

Computing the number of ways to select 3 from 6

Computing the number of ways to select 5 from 20

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Probability and Statistics

Mechanics Maths

Calculus

Geometry

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Compute the number of ways can select n element from N element of each of the following:
$n = 2, N = 5$
$n = 3, N = 6$
$n = 5, N = 20$