20 5 points A sale table has 6 different white shirts 4 diff

20. (5 points) A sale table has 6 different white shirts, 4 different yellow shirts, and 3 different blue shirts. Anne buys 4 of these shirts for her busband, how many different possible outcomes have at least 1 blue shirt and at least 1 white shirt? (A) 990 B) 11,304 (C) 11,256 (D) 700 (E) 471 (F) 16, 800 (G) 126 (B) 111 (J) 469 (K) 1,980 (L) none of the others

Solution

Since Anne took 4 shirts with atleast 1 blue and 1 white, and the total number of shirts is 13.

There are different possible ways of taking the shirts is

Case1: 1 white, 1 blue, 2 yellow.

The possible number of ways of doing this is 6(3)(6)=108

Case2: 1 White, 2 blue, 1 yellow

The possible number of ways of doing this is 6(3)(4)=72

Case 3: 1 White , 3 blue

The possible number of ways of doing this is 6(1)=6

Case 4: 2 White , 1 blue, 1 yellow

The possible number of ways of doing this is 15(3)(4)=180

Case 5: 3 White , 1 blue

The possible number of ways of doing this is 20(3)=60

Case 6: 2 White , 2 blue

The possible number of ways of doing this is 15(3)=45

Total number of ways is 108+72+6+180+60+45=471

Hence option E is corect