There are 15 seats in the first row of a theatre of which 6 are to be occupied. The number of ways of arranging 15 person so that no two persons are side by side is k+5 , then digit in unit's place in k is equal to___

Step-by-step solution

Let the six persons P₁, P₂, P₃, P₄, P₅ and P₆ be seated. x₁ is the number of seats to left of P₁, x₂ is the number of seats in between P₁ and P₂, , x₇ is the number of seats to right of P₆ such that x₁+x₂+x₃+ . .+x₇=9 . i.e., coefficient of x^9 in (1+x+x^2+ . . )^2 (x+x^2+x^3+ . )^5= ¹⁵⁻⁶⁺¹ C₆= ¹⁰ C₆ 6 persons can be arranged in 6! ways ¹⁰ P ₆ is the answer