# 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 Option 1) 3 Option 2) 36 Option 3) 66 Option 4) 108

As we learnt in

Theorem of Combination -

Each of the different groups or selection which can be made by taking r things from n things is called a combination.

$^{n}c_{r}=\frac{(n)!}{r!(n-r)!}$

- wherein

Where $1\leq r\leq n$

Urn A $\rightarrow$ 3 Red balls.

Urn B $\rightarrow$ 9 Blue balls

Number of ways $=^{3}C_{2}\times^{9}C_{2}=\frac{3\times 9\times 8}{2}=108$

Correct option is 4.

Option 1)

3

This is an incorrect option.

Option 2)

36

This is an incorrect option.

Option 3)

66

This is an incorrect option.

Option 4)

108

This is the correct option.

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