How many Permutation & Combination questions come in CAT Quant?

About 0.8 questions in a 22-question Quant section, worth roughly 2 marks. Permutation & Combination appeared in 19 of the 24 CAT papers from 2017 to 2025, 23 questions in all, which ranks it 18 of 25 Quant chapters.

Are Permutation & Combination questions in CAT MCQ or TITA?

65% of the Permutation & Combination questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.

What types of Permutation & Combination questions does CAT ask?

CAT keeps returning to 6 question shapes in Permutation & Combination: Building numbers out of digits; Handing out identical things; Selecting a group under conditions; Multiply the independent choices; Pairs, and the pigeonhole; The sum or mean of all rearrangements.

Permutation & Combination for CAT: Formulas, Weightage & Question Types

Numbers from digits, handing out identical things, and selecting under conditions.

Permutation & Combination formula sheet

Everything CAT needs from Permutation & Combination, in one place. Bookmark it for revision; the lesson in the app explains where each line comes from and when to reach for it.

Everything for this chapter, in one place.

The two tools


Order matters — arrangements	$^nP_r = \dfrac{n!}{(n-r)!}$
Order does not — selections	$^nC_r = \dfrac{n!}{r!\,(n-r)!}$
Symmetry	$^nC_r = {}^nC_{n-r}$
Edges	$^nC_0 = {}^nC_n = 1$
Link	$^nP_r = {}^nC_r \times r!$

When some objects are identical


Arranging $n$ with repeats $p, q, \dots$	$\dfrac{n!}{p!\,q!\cdots}$
Round a circle	$(n-1)!$
Any subset of $n$ distinct things	$2^n$

Identical objects into distinct boxes — stars and bars


$n$ identical into $r$ boxes, empties allowed	$^{n+r-1}C_{r-1}$
Each box at least one	$^{n-1}C_{r-1}$
Each box at least $k_i$	hand out the minimums first, then use the "empties allowed" form
An upper limit as well	count without it, then subtract the violations

Counting the complement


"At least one …"	total $-$ "none"
"At least one digit repeated"	total $-$ "all digits distinct"
Onto functions, $m$ elements to $n$	$n^m - {}^nC_1(n-1)^m + {}^nC_2(n-2)^m - \cdots$

Numbers from digits


Sum of all numbers from $n$ distinct digits, each used once	$(n-1)! \times (\text{sum of digits}) \times \underbrace{11\cdots1}_{n}$
Each digit appears in each place	$(n-1)!$ times
Leading zero	count freely, then subtract the arrangements that start with 0
Divisible by 3	the digit sum must be divisible by 3
Divisible by 6	digit sum divisible by 3 and last digit even

Paths and pairs


Lattice paths, $m$ right and $n$ up	$^{m+n}C_m$
Via an intermediate point	multiply the two legs
Handshakes among $n$	$^nC_2$
Pigeonhole	with $n$ items in $k$ boxes some box holds at least $\left\lceil \frac{n}{k} \right\rceil$

The 6 Permutation & Combination question types CAT repeats

Past CAT papers return to the same few shapes. Learn to recognise them and most questions become a known routine.

01
Building numbers out of digits
02
Handing out identical things
03
Selecting a group under conditions
04
Multiply the independent choices
05
Pairs, and the pigeonhole
06
The sum or mean of all rearrangements

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Permutation & Combination in CAT: quick answers

How many Permutation & Combination questions come in CAT Quant?: About 0.8 questions in a 22-question Quant section, worth roughly 2 marks. Permutation & Combination appeared in 19 of the 24 CAT papers from 2017 to 2025, 23 questions in all, which ranks it 18 of 25 Quant chapters.
Are Permutation & Combination questions in CAT MCQ or TITA?: 65% of the Permutation & Combination questions asked since 2017 were TITA (type in the answer, no negative marking). The rest were multiple choice.
What types of Permutation & Combination questions does CAT ask?: CAT keeps returning to 6 question shapes in Permutation & Combination: Building numbers out of digits; Handing out identical things; Selecting a group under conditions; Multiply the independent choices; Pairs, and the pigeonhole; The sum or mean of all rearrangements.

Permutation & Combination for CAT: Formulas, Weightage & Question Types

Permutation & Combination formula sheet

The 6 Permutation & Combination question types CAT repeats

Is Permutation & Combination costing you marks?

Permutation & Combination in CAT: quick answers

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