(i) If nP4 : nP5, = 1 : 2, find n.
(ii) If n–1P3 : n+1P3, = 5 : 12, find n.
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
nP4 : nP5 = 1:2
n – 4 = 2
n = 6
Hence, value of n is 6.
(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
n–1P3 : n+1P3, = 5 : 12
12
n = 8, 2.25
Since n cannot be 2.25 as it creates a negative factorial in denominator. Therefore,
n = 2.25 is not possible.
Hence, value of n is 8.
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