There are 10 men and 8 women in a department (a) In how many ways can the 10 men and 8 women be arranged in a row if three of the men (not any three, specified three) would like to stand together (i.e., no one else is allowed to stand in between any two of them) and none of the other 7 men would want to stand next to another man. (b) In how many ways can the 10 men and 8 women be arranged in row if no two women would like to stand next to each other (i.e., there should be at least one man standing in between any two women). (c) In how many ways can a committee consisting of 6 members be formed if the committee has to have at least three women.

There are 10 men and 8 women in a department (a) In how many ways can the 10 men and 8 women be arranged in a row if three of the men (not any three, specified three) would like to stand together (i.e., no one else is allowed to stand in between any two of them) and none of the other 7 men would want to stand next to another man. (b) In how many ways can the 10 men and 8 women be arranged in row if no two women would like to stand next to each other (i.e., there should be at least one man standing in between any two women). (c) In how many ways can a committee consisting of 6 members be formed if the committee has to have at least three women.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. There are 10 men and 8 women in a department
(a) In how many ways can the 10 men and 8 women be arranged in a row if three of the men (not any three, specified
three) would like to stand together (i.e., no one else is allowed to stand in between any two of them) and none of
the other 7 men would want to stand next to another man.
(b) In how many ways can the 10 men and 8 women be arranged in row if no two women would like to stand next to
each other (i.e., there should be at least one man standing in between any two women).
(c) In how many ways can a committee consisting of 6 members be formed if the committee has to have at least three
women.

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