CAT Quantitative Aptitude Questions | CAT Permutation and Combination Questions

The question is from Permutation and Combination. This is about selecting a card pack. Our task is to find out the number of ways of selecting five cards which contains all four suits. This section hosts a number of questions which are on par with CAT questions in difficulty on CAT Permutation and Combination, and CAT Probability.

Question 22: In how many ways can be select 5 cards from a card pack such that all 4 suits appear?

1. 52728
2. 405646
3. 685464
4. 4056

Explanatory Answer

Method of solving this CAT Question from Permutation and Combination: Simple Card Pack Selection

Each suit has 13 cards and one card can be selected from each suit in ¹³C₁ ways. For selecting 5 cards from a card pack we need to have two cards from one suit and 3 cards from the other three suits.
Suit which will have 2 cards can be selected in ⁴C₁ ways and two cards can be selected from that suit in ¹³C₂ ways. Overall 5 cards can be selected such that all 4 suits appear in ⁴C₁*¹³C₂*¹³C₁ = 4*13*13*13*78 = 685464 ways.

The question is "In how many ways can be select 5 cards from a card pack such that all 4 suits appear?"

Hence the answer is "685464"

Choice C is the correct answer.