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1 answer:
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Answer:
A. a) 24
A. b) 4
B. a) 40320
B. b) 576
Step-by-step explanation:
General formula for Permutations:
A. Concert seats: 2 couple --- total of 4 persons.
a) without restrictions
Since there are no restrictions, but that the order is important (John, Mary, Paul, Michelle isn't the same as Michelle, Mary, Paul, John), it's a permutation calculation.
Then we calculate the permutations of 4, out of 4, so...
24 different ways for them to sit.
b) couples together
Now, we can see the problem as having 2 levels of permutations, first the couples, then inside the couples.
There are 2 ways for the first level or order... couples AB or BA, so 2 possibilities.
Inside each couple, man then woman (MW) or woman then man (WM), so 2 possibilities there too on 2nd level.
Overall 2 * 2 = 4 ways to sit by couple.
B) Single file
a) without restrictions
Again, order is important, so another permutation, not a combination. And since we have no restriction, it can be any sequence.
We then have to calculate the number of permutations of 8 out of 8...
There are 40,320 ways these 8 kids can pass the door.
b) girls first.
So, the four girls have to enter first.... and these four girls can be in any order.. how many permutations? P(4,4)... so 24 as calculated above.
For the four boys, how many permutations? Yes, again P(4,4)... so 24 again.
Overall, we need to multiply the two... 24 x 24 = 576 ways if the girls enter first, followed by the boys.
Given:
The expression is .
To find:
The position of parentheses inserted in the expression to get the value 19
Step-by-step explanation:
We have,
Now,
There are more ways to apply the parenthesis, but we do not get 19.
And many more possibilities.
Therefore, the expression after inserting the parentheses is .
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