## A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\heartsuit$ and $\diamondsuit$, c

Question

A standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. Two of the suits ($\heartsuit$ and $\diamondsuit$, called ‘hearts’ and ‘diamonds’) are red, the other two ($\spadesuit$ and $\clubsuit$, called ‘spades’ and ‘clubs’) are black. The cards in the deck are placed in random order (usually by a process called ‘shuffling’). In how many ways can we pick two different cards

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2022-02-03T03:56:44+00:00
2022-02-03T03:56:44+00:00 1 Answer
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## Answers ( )

Answer:The number of ways to select 2 cards from 52 cards without replacement is

1326.The number of ways to select 2 cards from 52 cards in case the order is important is

2652.Step-by-step explanation:Combinations is a mathematical procedure to compute the number of ways in which

kitems can be selected fromndifferent items without replacement and irrespective of the order.[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]

Permutation is a mathematical procedure to determine the number of arrangements of

kitems fromndifferent items respective of the order of arrangement.[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]

In this case we need to select two different cards from a pack of 52 cards.

Compute the number of ways to select 2 cards from 52 cards without replacement as follows:

[tex]{n\choose k}=\frac{n!}{k!(n-k)!}[/tex]

[tex]{52\choose 2}=\frac{52!}{2!(52-2)!}[/tex]

[tex]=\frac{52\times 51\times 50!}{2!\times50!}\\=1326[/tex]

Thus, the number of ways to select 2 cards from 52 cards without replacement is

1326.Compute the number of ways to select 2 cards from 52 cards in case the order is important as follows:

[tex]^{n}P_{k}=\frac{n!}{(n-k)!}[/tex]

[tex]^{52}P_{2}=\frac{52!}{(52-2)!}[/tex]

[tex]=\frac{52\times 51\times 52!}{50!}[/tex]

[tex]=52\times 51\\=2652[/tex]

Thus, the number of ways to select 2 cards from 52 cards in case the order is important is

2652.