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Chapter 13: Q. 28 (page 855)

List all the combinations of 5 objects a,b,c,d,and etaken 2 at a time. What is C(5,2)?

Short Answer

Expert verified

The list of combinations is:

ab,ac,ad,ae,bc,bd,be,cd,ce,de.

The value of the given combination is 10.

Step by step solution

01

Step 1. Given information.

2 objects are taken at a time from 5 objects a,b,c,d,and eat a time.

The given combinations is C(5,2).

02

Step 2. Determine the list of combinations.

The list of combinations is:

ab,ac,ad,ae,bc,bd,be,cd,ce,de.

03

Step 3. Determine the value of combination.

We know that,

C(n,r)=n!(n-r)!r!

Using the above formula, we get

C(5,2)=5!(5-2)!2!=5!3!2!=5脳4脳3!3!脳2脳1=10

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