About crew consists of 8 men„ 3 of whom can row only on one side and two only on other side the number of ways in which the crew can be arranged if
Answers
Assuming 4 crews on each side.
3 specific crews must row on any of the 4 seats on one side.
Arrangement for the 3 crews = ⁴P₃ = (4 x 3 x 2 x 1 )/ 1 = 24 ways
1 specific crew can row on any of the 4 seats on the other side:
Arrangement for the 1 crew = ⁴P₁ = (4 x 3 x 2 x 1) / (3 x 2 x 1) = 4 ways
The rest of the 5 crews can sit anywhere they like:
Arrangement for the 5 crews = ⁵P₅ = (5 x 4 x 3 x 2 x 1) = 120 ways
Total number of arrangement = 24 x 4 x 120 = 11520 ways
Answer: There are 11520 ways
(1) 4 persons must sit in each side (as normally equal number of persons sits in each side).
(2) arrangements of the persons within a particular side are different.
select the 3 persons who sit on first side(1 way).
select the 2 persons who sit on second side(1 way).
There are 3 persons remaining. Select one person from them for the first side(3C1=3 ways). Now total number of persons in the first side becomes 4.
Remaining 2 persons can be selected for the second side only in one way. Now total number of persons in second side also becomes 4.
4 persons in first side can be arranged in 4! ways.
4 persons in second side canbe arranged in 4! ways.
Required number of ways
=3×4!×4!= 1728 no. of ways.