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Chapter 12: Q3. (page 641)

Determine whether the statement Cn,r=Pn,r is sometimes, always, or never true. Explain your reasoning.

Short Answer

Expert verified

The statement istrue when r = 0 or 1.

Step by step solution

01

Step 1. Given Information.

Given to check whether the statement Cn,r=Pn,r is sometimes, always, or never true.

02

Step 2. Calculation.

When n objects are available and r are to be picked then the number of combinations is given by Cn,r=n!n-r!r!

When n objects are available and r are to be picked then the number of permutations is given by Pn,r=n!n-r!

When Cn,r=Pn,r,

Cn,r=Pn,rn!n鈭�r!r!=n!n鈭�r!11r!=11r!=1

For the statement to be true, r!=1i.e., r=0or1.

03

Step 3. Conclusion.

Therefore, the statement is true when r = 0 or 1.

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