Management Aptitude Test 2014 Paper

(a) There are total of 10 persons of which ${\mathit{P}}_1$ is always selected and hence ${\mathit{P}}_4$ and ${\mathit{P}}_5$ are not be included in the arrangement
Now, person left = 10 - 3 = 7
(as ${\mathit{P}}_1$ is already selected and ${\mathit{P}}_4$ and ${\mathit{P}}_5$ are not selected)
∴ To select 4 persons from 7 persons
total ways = ${}_{}^7{\mathit{C}}_4^{}$
Also, these 5 persons can be arranged in 5! ways
∴ Required ways of arrangement = ${}_{}^7{\mathit{C}}_4^{}$ x 5!