Answer to Question #220864 in Statistics and Probability for Ann

Question

A sample of five marble is to be selected, without replacement and without regard to order, from a box that contains three red, four green, and six purple marbles. In how many ways can this be done if

(a) Exactly two of the marbles selected are to be red, two are to be green, and one is to be  purple?

 (b) All are red or purple?

 (c)  All are to be red or all are to be purple?

Answer 1

(a) $N=C_3^2*C_4^2*C_6^1=3*6*6=108.$

(b) $N=C_9^5=126.$

(c) $N=C_6^5=6.$