# many are odd? (d) howmany are uunupres -In how many ways can a party of 7 persons arrange themselves (a) in a row of 7 chairs?(b)3around a circular table?4. There are 3 boys and 2 girls. (a) In how many ways can 3 boys and 2 girls sit in a row? (b) In howmany ways can they sit in a row if the boys and girls are each to sit together? ( c) In how manyways can they sit in a row if just the girls are to sit together?How many different signals, each consisting of 6 flags hung in a vertical line, can be formed fromidentical blue flags?4Tdentical redcommittee consisting of 3 men and 2 women be chosen from 7men

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Step 1

Given that there are 3 boys and 2 girls. There are a total of 5 people.

(a) Since, there is no specification of gender, 3 boys and 2 girls can be arranged in 5! ways,

that is,

Step 2

(b) There only 2 possible ways to seat the group because boys and girls are each to sit

together.

The possible number of ways is calculated as shown below.

Step 3

Thus, there are 24 ways to make the boys and girls each to sit together.

(c) Here, the girls have to be seated together. Now, there are totally 4 objects, that is the

group of girls is considered as one objects, 3 boys and 1...

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