Answer:
Total number of ways will be 209
Step-by-step explanation:
There are 6 boys and 4 girls in a group and 4 children are to be selected.
We have to find the number of ways that 4 children can be selected if at least one boy must be in the group of 4.
So the groups can be arranged as
(1 Boy + 3 girls), (2 Boy + 2 girls), (3 Boys + 1 girl), (4 boys)
Now we will find the combinations in which these arrangements can be done.
1 Boy and 3 girls = [tex]^{6}C_{1}\times^{4}C_{3}=6\times4[/tex]=24
2 Boy and 2 girls=[tex]^{6}C_{2}\times^{4}C_{2}=\frac{6!}{4!\times2!}\times\frac{4!}{2!\times2!}=15\times6=90[/tex]
3 Boys and 1 girl = [tex]^{6}C_{3}\times^{4}C_{1}=\frac{6!}{4!\times2!}\times\frac{4!}{3!}=\frac{6\times5\times4}{3 \times2} \times4=80[/tex]
4 Boys = [tex]^{6}C_{4}=\frac{6!}{4!\times2!} =\frac{6\times 5}{2\times1}=15[/tex]
Now total number of ways = 24 + 90 + 80 + 15 = 209
