generals336
2021-08-21
Velsenw
Skilled2021-08-22Added 91 answers
(a)
Since there shouldn’t be a complete pair, we are allowed to choose at most 1 shoe from each pair.
Therefore, our choice can be made in the following way: first choose 8 pairs from the 10 pairs in the closet. this can be done in ways.
Then from chosen 8 pairs, choose one shoe from each.
This can be done in ways as there are 2 choices for each pair.
Therefore, total number of choices is .
The number of ways to randomly choose 8 shoes out of 20 is . Therefore,
(b)
For getting exactly one pair, we can first choose the pair which will appear completely. there are 10 ways of doin it.
Then we need to choose 6 shoes from 9 remaining pairs.
Proceeding as part(a) we see that there are ((9),(6))2^6 ways for this. Therefore, the total number is . Thus,
Result:
star233
Skilled2023-05-13Added 403 answers
alenahelenash
Expert2023-05-13Added 556 answers
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