Question:
Determine the number of 5-card combinations out of a deck of 52 cards if each selection of 5 cards has exactly one king.
Answer:
Total number of cards = 52
Number of king card in 52 cards = 4
Number of remaining cards other than the king card = 52 - 4 = 48
Now we have to select combination of 5 cards in which there is exactly on king card.
So total number of combination = 4C1 * 48C4
= (4*48*47*46*45)/(4*3*2)
= (48*47*46*45)/(3*2)
= (48*47*46*45)/6
= 8*47*46*45
= 778320
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