Question

There are 10 persons named P₁,P₂,P₃, … P₁₀. Out of 10 persons, 5 persons are to be arranged in a line such that in each arrangement P₁ must occur whereas P₄ and P₅ do not occur. Find the number of such possible arrangements. 

[Hint: Required number of arrangement =⁷C₄× 5!]

Answer 1

We know that,

ⁿC_r = 

According to the question,

There are 10 person named P₁, P₂, P₃, … P₁₀.

Number of ways in which P₁ can be arranged =5! =120

Number of ways in which others can be arranged,

⁷C₄ = 7!/(4!3!) = 35

Therefore, the required number of arrangement =C₄⁷ × 5

=35 x 120

=4200