Question

Three members (mary ,sue and tom of a 20-person office of carpooling so they insit on never working seperatly. that is whenever one of them is on a committe all three must be. How many committes of size 7 meet this requirment.

Answer 1

Answer:

2380 committees of size 7 meet the given requirement.

Step-by-step explanation:

The question is basically asking us to find the number of ways in which 7 persons can be selected in a committee, such that 3 members ( Mary, Sue and Tom ) are always included.

Now, there are a total of 20 persons in the office, out of which 3 members are always included in the committee.

So, 3 members can be selected in $3_C__3$ ways.

Now, 4 members are to be selected  out of the remaining 17  persons in the office.

So 4 members can be selected in $17_C__4$ ways.

And so the total number of ways of selecting 7-member committee with the given requirement = $3_C__3$ x $17_C__4$ = 2380 ways.