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2 answers:
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Answer:
(a) 40,320
(b) 576
Step-by-step explanation:
(a) We are asked to find the number of orders in which four girls and four boys can walk through a doorway single file if there are no restrictions.
Since there are 8 people in total, so they can walk in 8! ways.
Therefore, four girls and four boys walk through a doorway single file in 40,320 ways.
(b) To find the number of ways in which four girls and four boys can walk through a doorway single file if the girls walk through before the boys.
The total number of ways would be equal to product of 4 girls walking first and 4 boys walking after.
4 girls can walk first in 4! ways and boys can walk after in 4! ways as well.
Therefore, four girls and four boys can walk through a doorway single file if the girls walk through before the boys, in 576 ways.
Answer:
In improper form your solution will be . As a mixed fraction it will be
.
Step-by-step explanation:
The first thing we want to do here is to simplify this expression. After doing so, " a " and " b " should be multiplied to result in a possible improper fraction,
- Apply exponential rule "
"
= - Combine fractions
and
= - Multiply the fractions, and simplify further
= =
- This is out simplified expression
Now that we have this simplified expression, we can see that a = , and b =
. Therefore, multiplying the two we should receive the improper fraction as follows,
=
- Note that this is in improper form. If you want your solution in a mixed fraction, it will be
.