# (i) If n</su

(i) To find: the value of n

Formula Used:

Total number of ways in which n objects can be arranged in r places (Such that no object is replaced) is given by,

nPr nP5 = 20 × nP3.   20 = (n - 3)(n - 4)  (n - 8)(n + 1) = 0

n = 8, -1

We know, that n cannot be a negative number.

Hence, value of n is 8

(ii) To find: the value of n

Formula Used:

Total number of ways in which n objects can be arranged in r places (Such that no object is replaced) is given by,

nPr 16 × nP3 = 13 × n+1P3.   16n – 32 = 13n + 13

3n = 45

n = 15

Hence, value of n is 15.

(iii) To find: the value of n

Formula Used:

Total number of ways in which n objects can be arranged in r places (Such that no object is replaced) is given by,

nPr 2nP3 = 100 nP2   2n(2n - 1)(2n - 2) = 100 × n(n - 1)

4n(2n - 1)(n - 1) = 100 × n(n-1)  8n(n - 13) = 0

n = 0, 13

We know that n should be greater than zero.

Hence, value of n is 13

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