SNAP Permutations, Combinations and Probability Previous Year Questions

SNAP Permutations, Combinations and Probability PYQ, free to download as a 41-page PDF. The bank carries 24 solved questions from the 2006 to 2025 papers and takes roughly two days to work through, so split it across counting one day and probability the next.

Every question keeps the year it was asked and the options exactly as printed. An answer key follows the questions, then a full worked solution for all 24.

How the Answer Key Was Prepared

Worth stating plainly, because it is unusual. Symbiosis does not release an official answer key for SNAP, and the question papers we work from carry the questions only.

Every answer in this booklet was therefore worked out by our team from first principles, not copied from an official key. Each numeric answer was independently reproduced using exact fraction arithmetic and checked to land on exactly one of the four options, including the two questions where the honest answer is that none of the printed options is correct.

Each solution shows the full reasoning, so you can follow the working rather than take the letter on trust.

What the 24 Questions Cover

Permutations, Combinations and Probability sits inside the Quantitative, Data Interpretation and Data Sufficiency section, and this topic alone has produced at least one question in nearly every SNAP paper since 2006.

• Word and letter arrangements, including repeated letters and fixed-position vowels
• Distribution and grouping counts, such as splitting distinct items among people under a constraint
• Restricted seating and row arrangements, both circular and linear, where certain items must or must not sit together
• Conditional probability, including a Bayes'-rule question dressed up as a dice-and-groups story
• Classic probability engines, such as odds in favour, weighted lotteries, and the leap-year weekday question that reappears across MBA entrance exams

The Six Moves That Solve Almost All of Them

Across the 24 questions the same handful of moves keeps working. Naming them makes the section much faster.

• For "at least one" questions, work out the complement first. It is almost always the shorter route
• For "must stay apart" questions, arrange the free items first, then place the restricted ones into the gaps between them
• For "must stay together" questions, glue the group into one block, arrange the outer units, then arrange the block's own contents separately
• For overlapping conditions, such as two people each getting exactly one item, check for double counting and subtract it with inclusion-exclusion
• For a random selection that then produces an outcome, weight each path by its own probability before combining them, which is Bayes' rule even when the question never says so
• For a round table, remember the fixed group arranges in (n minus 1) factorial ways, not n factorial, because a full rotation is the same seating

When the Honest Answer Is "None of These"

Two of the 24 questions resolve to an option that simply says none of the given numbers is correct, and both are worth studying rather than skipped.

One asks how many dye combinations a paint company can create using at least one blue and one green dye from its stock. Working the count through independent nonempty and free choices gives 3,720, a number that appears nowhere among the four printed options.

The other asks for the probability of a month having exactly three fewer days than the longest month, which only February satisfies, giving 1 in 12, again absent from the choices. Forcing the nearest-looking number in either case costs the mark.

Two Questions Worth Doing First

If time is short, start here. Each teaches a move the rest of the set reuses.

2023, conditional probability. A die roll first picks one of three groups, then a girl is chosen from it. Weighting each group's chance of being picked against its own chance of yielding a girl, then applying Bayes' rule, is the fastest way through the whole conditional-probability family in this bank.

2019, restricted arrangement. Ten mechanics books and eight quantum physics books are placed in a row so that no two quantum physics books touch. Arranging the ten books first and counting the gaps between them, rather than trying to place every book directly, turns an intractable count into a single combination.

Watch Permutations, Combinations and Probability Solved for SNAP

Source: CATKing

How to Use the Answer Key and Solutions

Attempt the whole set before checking anything. The layout is built so an answer cannot be glimpsed by accident.

• Do all 24 in one timed sitting, allowing about ninety seconds each
• Mark the answer key in one pass, right or wrong only
• Read the solution for every miss and every lucky guess
• Each solution opens with a one-line quick solution, so you can stop there and retry

Traps These Questions Are Built Around

A handful of errors account for most lost marks here, and several questions exist only to catch them.

• Arranging distinct books or bars as if they were identical items, which changes the count entirely
• Forgetting the internal arrangement of a glued block after counting the outer units
• Skipping the overlap term when two conditions can both be true at once
• Mixing up odds in favour with plain probability
• Forcing the closest-looking option when the true answer is none of these

For the wider section, the SNAP Logical Reasoning Blood Relations PYQs and the SNAP General English topic notes cover the rest of the paper in the same format.