Question 98

If $$^nC_x = 56$$ and $$^nP_x = 336$$, then Find n and x?

$$^nP_r$$ = $$^nC_r$$*r!

$$^nP_x = 336$$

$$^nC_x *x!$$ =Β 336

x!=Β $$\ \frac{336}{56}$$

x!=6

x=3

$$^nC_x = 56$$

$$\ \ \frac{\ n!}{\left(n-x\right)!\times\ x!}\ =\ 56$$

$$\ \ \frac{\ n!}{\left(n-3\right)!\times\ 3!}\ =\ 56$$

n=8

$$\therefore$$ n= 8, x=3

C is the correct answer.

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