Suppose you have a set S of 5 women and 5 men.
(a) How many ways can you select a set of 5 people from S?
(b) How many ways can you select an equal number of women and men from S (either 0, 1,2, 3, 4, or 5 of each)?
(c) Do you notice anything and is it a coincidence? (Note: There is something here if you don't see it you are doing something wrong in a or b)
(a) How many ways can you select a set of 5 people from S?
(b) How many ways can you select an equal number of women and men from S (either 0, 1,2, 3, 4, or 5 of each)?
(c) Do you notice anything and is it a coincidence? (Note: There is something here if you don't see it you are doing something wrong in a or b)
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a. 10C5 = 10!/5!5!
b. 5Ck *5Ck for k = 0 to 5 yields 1, 25, 100, 100, 25 & 1
c. you can see for yourself !
b. 5Ck *5Ck for k = 0 to 5 yields 1, 25, 100, 100, 25 & 1
c. you can see for yourself !