Question

Nine people (Ann, Ben, Cal, Dot, Ed, Fran, Gail, Hal, and Ida) are in a room. Five of them stand in a row for a picture. In how many ways can this be done if Ann and Ben must be in the picture but not standing next to each other?

How many positive integers not exceeding 1000 are divisible by 4, 6, or 9? Compute all the way to the final answer – a single number

Answer 1

Ann and Ben are in picuture means we have to select them compulsory.

So we have to select 3 more people from remaining 7 people.

Total cases in which Ann and Ben are in picture

(5!=5*4*3*2*1=120)

= 4200

And we have have to subtract the cases in which Ann and Ben are next to each other.

Total number of cases in which  Ann and Ben are in picture and next to each other.

3! = 3*2*1=6

n! = n*(n-1)!

= 1680

Total required cases = 4200 -1680 = 2520

Total numbe of cases in which Ann and Ben must be in the picture but not standing next to each other = 2520