Agroup of school children consist of 25 boys and 18 girls. how many ways are there:
1. to arrange the children in a row
2. to arrange the children in a row with all the boys next to each other
3. to arrange the children in a row with all the boys next to each other and all the girls next to each other.
4. to choose a chess team of 6 from the group if 1. anyone can be chosen?
2. exactly 2 girls must be chosen?
3. at least 2 boys must be chosen?

Step-by-step explanation:

1. Number of boys in the group = 25

Number of girls in the group = 18

Total children = 25 + 18 = 43

Number of ways to arrange the children in a way = 43!

2. If we consider all the boys as an individual then number of ways children can be arranged = 19!

Number of ways boys can sit next to each other = 25!

So the number of ways can be arranged = 19!×25!

3. Number of ways boys can sit next to each other = 25!

Number of ways girls can sit next to each other = 19!

Then number of ways to arrange the children in a row with all boys next to each other and all the girls next to each other will be = 2 × 18! × 25!

4. 1. To choose a chess team if anyone can be chosen

=

= 6096454

4. 2. Exactly 2 girls must be chosen then number of ways

=

4. 3. At least two boys must be chosen

=

= 5863690

6mm^3 or .6cm^3

      216

      /   \

  36     6

  /   \     /

6     6   6

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