Q

# Try this! Three pairs of dice are rolled simultaneously. In how many different ways can the sum of the numbers appearing on the top faces of the 3 dices be 9?

Three pairs of dice are rolled simultaneously. In how many different ways can the sum of the numbers appearing on the top faces of the 3 dices be 9?

• Option 1)

18

• Option 2)

25

• Option 3)

22

• Option 4)

27

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As learnt in concept

Sum Rule of Association -

Let A can occurs in m ways and B can occurs in n ways and both cannot occur simultaneously. Then A or B can occurs in (m + n) ways.

- wherein

A or B means at least one of them.

Sum=9 can be written in several ways.

(i)    6+2+1    6 ways

(ii)    4+3+2    6 ways

(iii)    3+3+3    1 way

(iv)    2+2+5    3 ways

(v)    1+3+5    6 ways

(vi)    1+4+4    3 ways

25 ways

Option 1)

18

This option is incorrect.

Option 2)

25

This option is correct.

Option 3)

22

This option is incorrect.

Option 4)

27

This option is incorrect.

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