In how many different ways can six players be arranged in a line such that two of them, Ajit and Mukherjee,
In how many different ways can six players be arranged in a line such that two of them, Ajit and Mukherjee, are never together?
(a) 120 (b) 240 (c) 360 (d) 480
13 views
1 Answers
(d) Total no of ways of arrangement for six players = 6! Let us take Ajit and Mukerjee as one entity. So now there are (6 – 2 + 1) = 5 players
These 5 players can be arranged in 5! ways and Ajit and Mukerjee can be arranged among themselves in 2! ways. Thus, no of ways, when Ajit and Mukerjee are always together = 5 ! × 2!
Hence, no of ways when they are never together = Total no of ways – no of ways when they are always together
= 6 ! – (5 ! × 2 !) = 6 × 5 ! – (5 ! × 2 !) = 5 ! (6 – 2) = 480
13 views
Answered