Eight men and seven women are randomly assigned distinct numbers from 1 to 15. On an...
Eight men and seven women are randomly assigned distinct numbers
from 1 to 15. On
an average, how many pairs of consecutive numbers are assigned to
people of opposite sex?
Homework Answers
To assign consecutive people of opposite sex, the first person should be men, because if the first perope is women, then at the end there will be 2 men consecutively. So, if we start with men, all the odd places will be taken by men and even places by women. 8 men can be arranged in 8 places in 8! ways. Similarly, 7 women can be arranged in 7 places in 7! ways. So, the total number of ways is 8!*7!. So, the total number of pairs is (8!*7!)/2 ways.
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Eight men and seven women are randomly assigned distinct numbers
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