A contractor needs four carpenters; ten are sent from the union hall.
a. In how many ways can he pick his work crew?
ab, ac, ad, ba, bc, bd, ca, cb, cd, da, db ,dc
b. In how many ways the crew can be selected if John and Anna should be
included?
Can anyone help me with b please
oh never mind i have the answers
What did you get?
To answer question b, we need to consider that John and Anna are required to be part of the work crew.
Step 1: Select John and Anna
Since John and Anna need to be included, we can consider them as already selected for the crew. So, we are left with selecting the remaining two carpenters from the remaining eight (10 - 2 = 8) carpenters.
Step 2: Select the remaining two carpenters
We need to choose two carpenters from the remaining eight. Since the order of selection does not matter, we can use combinations to calculate the number of ways to select two carpenters from a group of eight.
To calculate the number of ways to select two carpenters from a group of eight, we can use the combination formula:
C(n, r) = n! / (r! * (n - r)!)
In this case, n is 8 (the number of carpenters left to choose from) and r is 2 (the number of carpenters to be selected). Let's calculate:
C(8, 2) = 8! / (2! * (8 - 2)!)
= 8! / (2! * 6!)
= (8 * 7 * 6!) / (2! * 6!)
= (8 * 7) / 2!
= 56 / 2
= 28
So, there are 28 ways to select the remaining two carpenters from the group of eight.
Step 3: Calculate the total number of ways
Since the selection of John and Anna is fixed, and there are 28 ways to select the remaining two carpenters, the total number of ways to form the work crew is:
Total ways = Number of ways to select John and Anna * Number of ways to select the remaining two carpenters
= 1 * 28
= 28
Therefore, there are 28 ways to select the work crew if John and Anna must be included.