PERMUTATIONS AND COMBINATIONS — MATHS STD 11 Science — Question
Gujarat BoardEnglish MediumSTD 11 ScienceMATHSPERMUTATIONS 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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