IPMAT Indore 2026 · Quantitative Ability · Question 20

IPMAT Indore 2026 previous year question on Probability, with the answer and a step-by-step solution.

ProbabilityModern MathsMultiple choiceMedium

Three dice are thrown simultaneously and the sum of the three numbers appearing on the top faces of the dice is found to be 10. The probability that these three numbers are distinct, is

A
\frac{3}{4}
B
\frac{2}{3}
C
\frac{3}{5}
D
\frac{1}{2}

Pick an option, then check.

Answer & solution

Answer: Option B

This is a conditional probability: the sample space is already restricted to sums of 10.

Step 1 — count all ordered triples summing to 10. Substituting a'=a-1 etc., we need a'+b'+c'=7 with each between 0 and 5:

\left( \genfrac{}{}{0pt}{}{9}{2}\right)-3\left( \genfrac{}{}{0pt}{}{3}{2}\right)=36-9=27

(The subtraction removes cases where one variable exceeds 5.)

Step 2 — count those with all three distinct. Find the sets of three distinct values from 1–6 summing to 10:

\{1,3,6\}, \{1,4,5\}, \{2,3,5\}

Each set can be arranged in 3!=6 ways:

3\times 6=18

Step 3 — divide.

P=\frac{18}{27}=\frac{2}{3}

Answer: Option 2 — \frac{2}{3}

Shortcut. The denominator is 27, not 216 — the sum of 10 is given, so it is conditional. Then list only the distinct-value sets (just three of them) and multiply by 6. The repeats you are excluding are \{2,2,6\}, \{4,4,2\}, \{3,3,4\} and \{1,1,8\} (impossible).

IPMAT Indore 2026 · Quantitative Ability · Question 20

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