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Visual Solutions

10 step-by-step animated solutions for Permutations & Combinations. Each solution breaks the problem into visual clips with key insights.

PYQ 2024 · Jan 31 Shift 2Easy4 steps

The number of ways in which 21 identical apples can be distributed among three children such that each child gets at least 2 apples, is

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PYQ 2024 · Jan (1 Feb) Shift 1Standard4 steps

n

is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then

n

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PYQ 2023 · Jan 24 Shift 2Standard4 steps

The number of integers, greater than 7000 that can be formed, using the digits 3, 5, 6, 7, 8 without repetition, is

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PYQ 2023 · Apr 6 Shift 2Standard4 steps

All the letters of the word PUBLIC are written in all possible orders and these words are written as in a dictionary with serial numbers. Then the serial number of the word PUBLIC is

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PYQ 2024 · Apr 6 Shift 1Standard4 steps

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is

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PYQ 2023 · Apr 10 Shift 2Standard4 steps

Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is

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PYQ 2023 · Apr 15 Shift 1Standard4 steps

The total number of three-digit numbers, divisible by 3, which can be formed using the digits 1, 3, 5, 8, if repetition of digits is allowed, is

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PYQ 2023 · Apr 8 Shift 1Tricky4 steps

The number of ways, in which 5 girls and 7 boys can be seated at a round table so that no two girls sit together, is

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PYQ 2024 · Apr 4 Shift 1Tricky4 steps

There are 5 points

P_1, P_2, P_3, P_4, P_5

AB

A

B

, of a triangle

ABC

. Similarly there are 6 points

P_6, P_7, \ldots, P_{11}

BC

P_{12}, P_{13}, \ldots, P_{18}

CA

. The number of triangles that can be formed using the points

P_1, P_2, \ldots, P_{18}

as vertices, is:

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PYQ 2023 · Apr 8 Shift 1Tricky4 steps

The number of arrangements of the letters of the word "INDEPENDENCE" in which all the vowels always occur together is

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Sequence & Series

Binomial Theorem