(Q). In how many ways batting order of 11 players can be made out of 15 players if Rohit is always selected ?
Sol:- Since Rohit is always selected so we are to select 10 players out of remaining 14 players which can be done in ¹⁴C₁₀ ways.
Now these 11 players can be arranged in 11! ways.
Hence total number of ways = ¹⁴C₁₀.11! Answer
(Q). In how many ways 5 distinct volume of chemistry & 7 distinct volume of botany books can be arranged on a bookshelf such that all the chemistry books & all the botany books are together ?
Sol:-
chemistry books within bunch 1 can be arranged in 5! ways. Botany books within bunch 2 can be arranged in 7! ways. Now these 2 bunches can be arranged in 2! ways.
Hence total number of ways = 5!.7!.2! Answer
(Q). In how many ways 15 students can be arranged in a row such that A is always between B and C ?
Sol:- 15 students without any condition can be arranged in 15! ways.
In these 15! ways following combination of A, B & C will be :-
So out of 6 arrangement of A, B, C we get 2 favourable cases.
i.e.
(Q). In how many ways 15 student can be arranged in a row such that p is always before q and r is always before s ?
Sol:- p, q, r, s can be arranged in 4! = 24 ways.
out of these 24 ways favourable cases are:-
So out o 24 ways 6 favourable ways are there
i.e.