Out of 10 persons
Question:

Out of 10 persons P1P2,…, P10, 5 persons are to be arranged in a line such that in each arrangement P1 must occur whereas P4 and P5 do not occur. The number of such arrangements is ___________.

Solution:

Since out of 5 to be selected, P1 is fix i.e P1 must occur.

⇒ we need to select 4 person out of 9 remaining.

Now, out of remaining 9, P4 and P5 do not occur

⇒ Available options are 7

⇒ Number of such arrangement

7C4 ×  5!   (since 5 persons in line can be arranged in 5! ways.)