A boat is to be manned by eight men of whom 2 can only row on bow side and 3 can only row on stroke side, the number of ways in which the crew can be arranged is
A.
4360
B.
5760
C.
5930
D.
None of these
Answer :
5760
Solution :
First we have to select 2 men for bow side and 3 for stroke side. The number of selections of the crew for two sides $$ = {\,^5}{C_2} \times {\,^3}{C_3}$$
For each selection there are 4 persons on both sides, who can be arranged in $$4! \times 4!$$ ways. Required number of arrangement
$$ = {\,^5}{C_2} \times {\,^3}{C_3} \times 4!\, \times 4! = 5760$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
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