In how many ways can 3 cards of same colour be selected from a well sh

1.	In how many ways can 3 cards of same colour be selected from a well shuffled pack of 52 cards?
Answer» In a pack of 52 cards, there are (13 spade + 13 club) 26 cards of black colour and (13 heart + 13 diamond) 26 cards of red colour. ∴ From a well shuffled pack of 52 cards, 3 cards of same colour can be selected In ²⁶C₃ + ²⁶C₃ ways. ∴ Total combinations = ²⁶C₃ + ²⁶C₃ = \(\frac{26×25×24}{3×2×1}+\frac{26×25×24}{3×2×1}\) = 2600 + 2500 = 5200

In how many ways can 3 cards of same colour be selected from a well shuffled pack of 52 cards?

Answer»

In a pack of 52 cards, there are (13 spade + 13 club) 26 cards of black colour and (13 heart + 13 diamond) 26 cards of red colour.

∴ From a well shuffled pack of 52 cards, 3 cards of same colour can be selected

In ²⁶C₃ + ²⁶C₃ ways.

∴ Total combinations = ²⁶C₃ + ²⁶C₃

= \(\frac{26×25×24}{3×2×1}+\frac{26×25×24}{3×2×1}\)

= 2600 + 2500 = 5200