If nPr = 120 nCr then r is equal to—Select one:a. 7b. 5c. 4d. 6
Question
If nPr = 120 nCr then r is equal to—Select one:a. 7b. 5c. 4d. 6
Solution
The given equation is nPr = 120 nCr.
The formula for nPr (permutation) is n! / (n-r)!. The formula for nCr (combination) is n! / r!(n-r)!.
So, we can write the given equation as: n! / (n-r)! = 120 * [n! / r!(n-r)!]
By simplifying, we get: 1 / (n-r)! = 120 / r!(n-r)!
This simplifies to: r! = 120
The value of r that satisfies this equation is 5 because 5! = 120.
So, the answer is b. 5.
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