Question

Suppose we want to choose 6 colors if the order is taken from 9 distinct colors

how many ways could this be done if the order of the choices is taken into consideration?

how many ways can this be done if the order choices is not taken into consideration?

Answer #1

We want to choose 6 colours from 9 distinct colours.

When the order is taken into consideration, we take a permutation of the 6 colours among 9 colours.

Number of ways this can be done = 9P6

= (9 !)/(9-6)!

= 9 * 8 * 7 * 6 * 5 * 4 = 60480

When the order is taken into consideration, this can be done in 60480 ways.

When the order is not taken into consideration, we take a combination of the 6 colours among 9 colours.

Number of ways this can be done = 9C6

= (9 !)/{(9-6)! * 6!}

= 9! / (6! * 3!) = 84

When the order is not taken into consideration, this can be done in 84 ways.

Suppose we want to choose 5 colors, without replacement, from 13
distinct colors. (a) How many ways can this be done, if the order
of the choices matters? (b) How many ways can this be done, if the
order of the choices does not matter?

Suppose we want to choose 5 letters, without replacement, from
13 distinct letters.
How many ways can this be done, if the order of the choices does
not matter?
How many ways can this be done, if the order of the choices
matters?

Probability Combinations -
A box of colored crayons contains 15 distinct colors. In how
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Q15: Suppose a car you want to buy has five choices for interior
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What can be done to limit the number of combinations without
limiting customer choice?

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Of these 9 inhabitants, 5 are knights, namely A, B, C, D, and
E.
Of these 9 inhabitants, the other 4 are knaves, namely W, X, Y, and
Z.
a. How many ways can the photographer choose 6 of these 9
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b. How many ways can the photographer choose 6...

How many ways can we pick three distinct integers from {1,2,
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In how many ways can we place n distinct objects into k distinct
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How many ways can we put 14 identical balls into 5 distinct bins
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1) How many 9 digits can be formed from the integers 5 5 6 6 6 2
8 9 7?
2) 9 candidates seek the nomination for a political party. In
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How many ways can we order the letters in SEVENTEEN? (Hint: Not
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