(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.


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