a driver comes to pick up members of your family (20 members) for a family reunion. the van holds 7 people not including the driver. assuming none of the babies will be riding (2 babies in the group of 20) how many different ways can 7 people be chosen to ride in the van?
21
To find the number of different ways 7 people can be chosen from a group of 20 members, we can use the concept of combinations.
The formula for combinations is given by:
C(n, r) = n! / (r!(n-r)!)
Where n is the total number of members and r is the number of members to be chosen.
In this case, we have 20 members in the family, excluding the 2 babies, which leaves us with 20 - 2 = 18 eligible members to choose from. We need to choose 7 people to ride in the van.
Using the formula for combinations, we can calculate the number of ways:
C(18, 7) = 18! / (7!(18-7)!)
= (18! / 7!11!)
= (18 * 17 * 16 * 15 * 14 * 13 * 12) / (7 * 6 * 5 * 4 * 3 * 2 * 1)
= 19,448
Therefore, there are 19,448 different ways to choose 7 people from a group of 20 members, excluding the 2 babies, to ride in the van.