Question

Suppose we want to choose 7 colors, without replacement, from 11 distinct colors.
(a) How many ways can this be done, if the order of the choices is not taken into consideration?
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(b) How many ways can this be done, if the order of the choices is taken into consideration?​

Answer 1

Answer:

330 ways ;

1663200 ways

Step-by-step explanation:

Choosing 7 colors from 11 distinct colors;

If order isn't taken into consideration :

We use combination :

nCr = n! ÷ (n-r)!r!

11C7 = 7! ÷ (11 - 7)!7!

11C7 = 11! ÷ 4!7!

11C7 = 11 * 10 * 9 * 8) / 4 * 3 *2 *1

11C7 = 7920 / 24

11C7 = 330 ways

If the order is taken into consideration :

We use permutation :

nPr = n! ÷ (n - r)!

11P7 = 11! ÷ (11 - 7)!

11P7 = 11! / 4!

11P7 = (11 * 10* 9 * 8 * 7* 6 * 5)

11P7 = 1663200 ways