Combinations

[rguduputi]

Problem –


Team size = 8 (Includes CEO, CFO and 6 other executives)

Mandate – A Committee must not include both CEO and CFO. Meaning a Committee can have either CEO or CFO. Not both.

Question - How many possible 5 member committees are possible?



My approach-

Total 5 member committee out of 8 Execs = Total Numberl 5 member committes (all) (5 choose 8) - Invalid number of committes


I got total committes as - 5 choose 8 = 8c5 = 8c3 = 8x7x6/6 = 56


We need to subtract the invalid Committee that have both CEO and CFO. Need help.

Thanks,
Ram



T

[kevin]

We need to subtract the invalid Committee that have both CEO and CFO. Need help.

How many ways are there of choosing the other 3 members? 6C3=6x5x4/3!=20

Alternatively,

CEO only 6C4=6C2=15
CFO only 15
neither 6C5=6C1=6
total 36