(i) If If 5Pr = 2 × 6Pr–1, find r.
(ii) If 20Pr = 13 × 20Pr–1, find r.
(iii) If 11Pr = 12Pr–1, find r.
(i) To find: the value of r
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
5Pr = 26Pr-1
r = 10, 3
Hence, value of r is 3, 10
(ii) To find: the value of r
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
20Pr = 1320Pr-1
21 – r = 13
r = 8
Hence, value of r is 8.
(iii) To find: the value of r
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
11Pr = 12Pr-1
(r - 16)(r - 9) = 0
r = 16, 9
Since r cannot be 16 as it creates a negative factorial in denominator. Therefore,
r = 16 is not possible.
Hence, value of r is 9.