9 chairs numbered 1 to 9. 3 women and 4 men wish to occupy one chair each. First the women will choose the chairs from amongst the chair marked 1 to 5, then the men select chairs from amongst the remaining. what is the possible number of arrangements?
The answer should be 150, but i got 1440 instead can someone tell me how to get the correct answer?
First, the 3 women must choose amongst the 5 first chairs. The number of possible ways is given by the binomial coefficient Binomial(n, k) (or "n choose k") with n=5 and k=3, which is equal to 10. This give you the number of ways to seat the 3 women when 5 chairs are available. After that, there are 6 seats remaining since 3 have are now occupied, and the 4 men must choose among these remaining seats. The number of ways to seat the 4 men when 6 chairs are available is Binomial(6, 4) = 15.
Now these two processes happen one after the other, so that the number of possibilities for your scenario is simply the multiplication of both, i.e., 10*150=150. Indeed, your first find seats for women (10 configurations), and for each possible configuration, there are 15 ways to seat the men, so that 150 configurations in total to accommodate both women and men.
