Combinations

[Cook10]

Hello, I was wondering if someone could help me and tell me if I am on the right track?
a.) In how many different ways could a family with 40 people choose 15 to attend a wedding? (1 mark)

40C15
= 4.022534506 x10

b.) In how many of these cases would Aunt Shirly and Uncle Sal both be attending?

2 x 38C13
= 1.082990059 x 10

 

[pka]

a.) In how many different ways could a family with 40 people choose 15 to attend a wedding? (1 mark)
40C15= 4.022534506 x10

b.) In how many of these cases would Aunt Shirly and Uncle Sal both be attending?

a) is correct
b) should be \(\mathcal{C}_{13}^{38}\) see here You need to learn how to use WolframAlpha.
For b) we just think of the two are chosen so we pick thirteen more.

 

[Steven G]

40C15 = 4.022534506 x10 is not correct. Yes, the 40C15 is correct! But how can that equal 4.022534506 x10 = 40.22534506 which is not a whole number. This makes me think that you have no idea what a combination is. A combination MUST be a whole number! Maybe you meant to write 40C15 = 4.0225345056 x10^10? But you did not!

2 x 38C13 = 1.0829900592 x 10 = 10.82990059 which is not an integer! Again perhaps you meant to write 2x38C13 = 1.0829900592 x 10^10?