Chapter 13: Q. 27 (page 855)

List all the combinations of 5 objects $a, b, c, d$ , and $e$ taken 3 at a time. What is $C (5, 3)$ ?

Short Answer

Expert verified

The list of combinations is:

$a b c, a b d, a b e, a c d, a c e, a d e, b c d, b c e, b d e, c d e .$

The value of the given combination is 10.

Step by step solution

Step 1. Given information.

3 objects are taken at a time from 5 objects $a, b, c, d,$ and $e$ at a time.

The given combinations is $C (5, 3)$ .

Step 2. Determine the list of combinations.

The list of combinations is:

$a b c, a b d, a b e, a c d, a c e, a d e, b c d, b c e, b d e, c d e .$

Step 3. Determine the value of combination.

We know that,

$C (n, r) = \frac{n!}{(n - r)! r!}$

Using the above formula, we get

$\begin{array}{rcl} C (5, 3) & = & \frac{5!}{(5 - 3)! 3!} \\ = & \frac{5!}{2! 3!} \\ = & \frac{5 \times 4 \times 3!}{2 \times 1 \times 3!} \\ = & 10 \end{array}$

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List all the combinations of 5 objects $a, b, c, d$ , and $e$ taken 3 at a time. What is $C (5, 3)$ ?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the list of combinations.

Step 3. Determine the value of combination.

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List all the combinations of 5 objects a,b,c,d, and etaken 3 at a time. What isC(5,3)?

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Determine the list of combinations.

Step 3. Determine the value of combination.

One App. One Place for Learning.

Most popular questions from this chapter

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List all the combinations of 5 objects $a, b, c, d$ , and $e$ taken 3 at a time. What is $C (5, 3)$ ?