Each of the 7 children, in turn throws a ball once at a target. Calculate the number of ways the children can be arranged in order to take the throws.

Question

Given that 3 of the children are girls and 4 are boys, calculate the number of ways the children can be arranged in order that
a. successive throws are made by boys and girls alternately,
b. a girl taken the first throw and a boy takes the last throw.

Answer 1

no. of ways the children can be arranged to take the throws:
7p7 = 5040 ways.

for successive throws:
4p4 * 5p3 = 144 ways

for girl takes the first and boy the last:
3p1 * 5p5 *4p*1 = 1440 ways