Genie_math

Total ten pair of gloves are there. If I choose five gloves at random then whats the probability that there is at least one matched pair? What is the probability that I pick at least one right glove and one left glove?

I need to find the coefficient of x^18 y^32 in (x+y)^50. I understand that we have to use the binomial theorem. I know how to find the coefficient for example x^18 but here we have "x" as well as "y" which I have no idea about.

There are eighteen guard posts. How many ways can 25 not indistinguishable (That is, they are distinguishable.)guards be distributed to the guard posts, so that no post is empty? Try - (25 choose 18) ??

Wouldnt it be from 20 gloves as we have 10 pairs. So for first glove we can pick any. [19 remaining] For second glove we have to select from 18 which are different - 18/19 3rd glove - 16/18 4th glove - 14/17 5th glove - 12/16 ...

I couldnot find the Q i posted that's why ... i replied there with some queries. Thank You for replying

How many monomials appear in the expansion of (x + y + z)^75?

Ohk so it will be - 1st glove - 20 2nd glove - 18/19 3rd glove - 17/18 4th glove - 16/17 5th glove - 15/16 Total probability = 1 - the probability of above things right ??