There are two urns. Urn $$A$$ has 3 distinct red balls and urn $$B$$ has 9 distinct blue balls. From each urn two balls are taken out at random and then transferred to the other. The number of ways in which this can be done is
A.
36
B.
66
C.
108
D.
3
Answer :
108
Solution :
Total number of ways $$ = \,{\,^3}{C_2} \times {\,^9}{C_2}$$
$$ = 3 \times \frac{{9 \times 8}}{2} = 3 \times 36 = 108$$
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
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is