Question

Decide whether the exercise involves permutations or​ combinations, and then solve the problem. Marbles are being drawn without replacement from a bag containing 1414 marbles. ​(a) How many samples of 44 marbles can be​ drawn? ​(b) How many samples of 22 marbles can be​ drawn? ​(c) If the bag contains 44 ​yellow, 22 ​white, and 88 blue​ marbles, how many samples of 33 marbles can be drawn in which all marbles are​ blue? Does the problem involve permutations or​ combinations?

Answer 1

Combinations

Explanation:

Given that marbles are drawn without replacement from a bag containing 14 marbles

Since it is without replacement and also order does not matter, we find that only combinations can be used here.

a) 4 marbles can be drawn from total 14 marbles in
`14C4 = 1001`

b) 2 marbles can be drawn in
`14C2 = 91`

c) If 4 yellow, 2 white and 8 blue, 3 blue marbles can be drawn in

`8C3 =56`

This problem involves combinations.