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.

Answer 1

Given that, P₁ , P₂ , …, P₁₀ , are 10 persons, out of which 5 persons are to be arranged but P, must occur whereas P₄ and P₅ never occurs.

As P, is already occurring w’e have to select now 4 out of 7 persons.

.'. Number of selections = ⁷C₄ = 35 Number of arrangements of 5 persons = 35 x 5! = 35 x 120 = 4200