Number of spade cards
=13, number of kings
=4Prime numbered cards are
2,3,5 and 7
So, total primes cards = 4 suits
×4numbers
⇒16 cards
But, a single card can be both a king and a spade or a prime and a spade.
So, the number of favourable outcomes.
Case I Spade that is not a king or prime
=13−1−4=8Case II King that is not a spade or prime = 3
Case III Prime card that is not a spade or king
=16−4=12So, total favourable cases
⇒‌‌8×3×12=288and total number of ways to choose 3 cards from 52 cards
=‌52C3=‌=‌=22100Thus, required probability
=‌=‌