If n C r -5 and n P r -120- then determine the value of n - r-A- 5-3B- 4-2C- 6-4D- 7-4E- 5-4

The correct option is E 5, 4 Soln: ^nP_r/^nC_r = 120/5 = 24 ^nC_r = (^nP_r)/(r!) ^nP_r/[^nP_r/r!] = 24 r! = 24 r = 4 Given ^nP_r = 120 ^nP_4 = 120 n!/(n 4)! ...

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Quantitative Aptitude

Combination

If n C r =5 a...

Question

If $^{n}$ C $_{r}$ = 5 and $^{n}$ P $_{r}$ = 120, then determine the value of n, r.

5, 3

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4, 2

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7, 4

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6, 4

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5, 4

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Solution

The correct option is E 5, 4
Soln: $\frac{^{n} P_{r}}{^{n} C_{r}}$ = $\frac{120}{5}$ = 24

$^{n}$ C $_{r}$ = $\frac{(^{n} P_{r})}{(r!)}$

$\frac{^{n} P_{r}}{[\frac{^{n} P_{r}}{r!}]}$ = 24

r! = 24

r = 4

Given $^{n}$ P $_{r}$ = 120

$^{n}$ P $_{4}$ = 120

$\frac{n!}{(n - 4)!}$ = 120

n(n-1)(n-2)(n-3) = 120

n = 5

Hence option (e)

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If nCr = 5 and nPr = 120, then determine the value of n, r.

The correct option is E 5, 4 Soln: nPrnCr = 1205 = 24 nCr = (nPr)(r!) nPr[nPrr!] = 24 r! = 24 r = 4 Given nPr = 120 nP4 = 120 n!(n−4)! = 120 n(n-1)(n-2)(n-3) = 120 n = 5 Hence option (e)

If $^{n}$ C $_{r}$ = 5 and $^{n}$ P $_{r}$ = 120, then determine the value of n, r.