Respuesta :
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 k items can be selected from n different 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 k items from n different 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.
- Two cards are selected without replacement:
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.
- Two cards are selected and the order matters.
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.
