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,

ⁿP_r

¹⁵P_r–1 : ¹⁶P_r–2, = 3 : 4

Since r cannot be 21 as it creates a negative factorial in denominator. Therefore,
is not possible.

Hence, value of r is 14