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Chapter 13: Q. 27 (page 855)

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

Short Answer

Expert verified

The list of combinations is:

abc,abd,abe,acd,ace,ade,bcd,bce,bde,cde.

The value of the given combination is 10.

Step by step solution

01

Step 1. Given information.

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

The given combinations is C(5,3).

02

Step 2. Determine the list of combinations.

The list of combinations is:

abc,abd,abe,acd,ace,ade,bcd,bce,bde,cde.

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

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