in a group of 6 boys and 4 girls, four children are to be selected. in how many different ways can they be selected such that at least one boy should be there?
Answer:
To find the number of ways to select 4 children from a group of 6 boys and 4 girls such that at least one boy should be there, we can use the principle of inclusion-exclusion.
The number of ways to select 4 children from a group of 6 boys and 4 girls is given by:
C(10,4) = 10! / (4! * (10-4)!) = 210,
The number of ways to select 4 children from only the 4 girls is given by:
C(4,4) = 4! / (4! * (4-4)!) = 1,
So, the number of ways to select 4 children such that no boy is included is 1.
To find the number of ways to select 4 children such that at least one boy is included, we subtract the number of ways in which no boy is included from the total number of ways:
C(10,4) - C(4,4) = 210 - 1 = 209,
Therefore, there are 209 different ways to select 4 children from a group of 6 boys and 4 girls such that at least one boy should be there.