# Questionbank: Permutation and Probability

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Simple Card Pack Selection

## Card Pack - Selection

Q.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

Choice C. 685464

## Detailed Solution

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.

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