Question

Ignoring suits and considering values only, how many arrangements of a deck of cards are there such that no two picture cards are consecutive?

Answer 1

ANSWER :-

Here we need to find in how many arrangements of a deck of cards are there such that no two picture cards are consecutive

There are 4 suits (Clubs, Hearts, Diamonds, and Spades) and there are 13 cards in each suit (Clubs/Spades are dark, Hearts/Diamonds are red)

- Without substitution implies the card IS NOT returned to the deck.

by ignoring suits.

no two picture cards are consecutive

There are 52 cards in a standard deck of cards

There are 4 of each card (4 Aces, 4 Kings, 4 Queens, etc.)

The probability of getting the first card is 13/52=1/4

The probability of getting the second heart is 12/51

which are 7 cards in 4 suits

28 total

Therefore in 28 arrangements of a deck of cards are there such that no two picture cards are consecutive.

Thank you.