AryamaDuttaSaikia wrote:
How many 5 letter words ( with or without meaning) can be formed using all the following 5 letters P,Q,R,S,and T so that letter P is to the left of
letter R?
(A) 120
(B) 60
(C) 48
(D) 24
(E) 12
We can solve this qustion by 2 methods,
Method 1: Total combinations for 5 letters = 5! = 120
As there is no bias in counting the combinations, half of the combinations will have R to the left of P and half of them to the right of P.
Thus possible combinations = 120/2 = 60. B is the correct answer.
Method 2:The combinations possible are:
PRQST, combinations of RQST = 4! =24
QPRST, combinations = 3C1*3!, 3C1 taken to account for the fact that instead of Q we can also take S or T
QSPRT, combinations = 2!*2!*3C2, 3C2 taken to account for the fact that instead of QS we can also take ST or QT, 2! each to take into account permutations for QS and RT
QSTPR, combinations = 3!*1, 3! to account for permutations for QST
Thus, the total combinations possible = 4!+3C1*3!+2!*2!*3C2+3! = 24+18+12+6=60. B is the correct answer.