Permutation and Combinations — Maths STD 11 Science — Question
CBSE BoardEnglish MediumSTD 11 ScienceMathsPermutation and Combinations1 Mark
MCQ
If $\ ^\text{n}\text{P}_5 = 60\ ^\text{n-1}\text{P}_3,$ the value of $n$ is:
A
$6$
✓
$10$
C
$12$
D
$16$
✓
Answer
Correct option: B.
$10$
Given that $\ ^\text{n}\text{P}_5 = 60\ ^\text{n-1}\text{P}_3,$
We know that $\text{P}(\text{n, r}) = \ ^\text{n}\text{P}_r = \frac{\text{n!}}{(\text{n-r})!}$
Now, apply the formula on both sides to get the value of $n.$
$\frac{\text{n!}}{(\text{n}-5)!} = 60 \bigg[\frac{(\text{n}-1)!}{(\text{n}-1)-3!}\bigg]$
On solving the above equation,
we get $n= -6$ and $n=10.$
Since the value of $n$ cannot be negative, the value of $n$ is $10.$
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