Solution for Section 6.4 Question 4b
4. b) Consider the possible dish combinations in three parts:
- you could choose four dishes that do not include either of the pork dishes (choose 4 out
of 25), or
- you could have the first pork dish and then choose three other dishes excluding the
second pork dish (choose 3 out of 25), or
- you could have the second pork dish and then choose three other dishes excluding the
first pork dish (choose 3 out of 25).
Since these three situations cannot overlap, you can apply the addition rule.
The total number of ways in which to choose four main dishes which contain at most one
of the two pork dishes is
( |
25 |
) |
+ |
( |
25 |
) |
+ |
( |
25 |
) |
= 12650 + 2300 + 2300 = 17250. |
| 4 |
3 |
3 |
Back to Section 6.4