Maths - Statistics and Combinations.?

Question

A restaurant owner has 45 dishes on his menu. How many combinations are there that include dish numbers 4, 32, 18, 19, and 29 but not dish number 1.

The way I see it, we can use nCr and calculate it this way, which would give me n = 45, r = 5 so the number of combinations is 1,221,759, but the 'does not include dish number 1' throws me. Is this still correct?

M3 · Accepted Answer

5 dishes to be included & 1 to be excluded is *fixed*
there are 39 other dishes, each of which can either be included or excluded,
thus # of combos = 2^39 <---------

note that this is also the sum of the binomial coefficients
39c0 + 39c1 + 39c2 + ....39c39

Maths - Statistics and Combinations.?

1 Antwort