Question

Out of 10 persons P₁, P₂,..., 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 ___________.

Answer 1

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.)