The Student Room Group

Stats question

The question is '8 people, including Kathy, David and Harpreet, are planning a theatre trip.

Four of the groups are chosen at random, without regard to order. Find the probability these four people include Kathy and David but not Harpreet'.

The answer is 5C2/8C4 or 1/7

I don't understand where the 5C2 has come from - it would be great if someone could explain it please
Reply 1
The probability is being found by number of possible combinations in this circumstance (with Kathy and David but not Harpreet) in the group of 4 divided by the total number of combinations 8C4

As is it given David and Kathy are in the group of 4 that leaves 6 people left in the group of 8 people with 2 more who can join the group of four. As this situation requires one person (Harpreet) to not be in the group of 4 that leaves 5 people who could fill those 2 spaces in the group of 4 so it is 5C2
once K & D have been selected that leaves 6 candidates for the other two places. However, H is excluded so that leaves 5 valid candidates for the 2 remaining places.
so 5C2 is the number of suitable groups of 4.

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