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3 years ago

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Suppose we want to choose 5 objects, without replacement, from 13 distinct objects. (a) How many ways can this be done, if the o

rder of the choices is not taken into consideration? (b) How many ways can this be done, if the order of the choices is taken into consideration?

1 answer:

Arisa [49]3 years ago

8 0

Answer:

A. 1, 287 ways

B. 154,440 ways

Step-by-step explanation:

A. We want to choose 5 objects from a total 13, without considering the order in which they are chosen.

The correct way to do this is by using the combination formula since order is not considered;

Thus we have ; 13 C 5 read as 13 combination 5;

Mathematically, n C r is ; n!/(n-r)!r!

Thus, we have ;

13!/(13-8)!8! = 13!/5!8! = 1,287 ways

B. By considering order, we shall be using the permutation formula;

Mathematically n P r = n!/(n-r)!

Read as n permutation r;

Using the numbers involved, we have ; 13 P 5

= 13!/(13-5)! = 13!/8! = 154,440 ways

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