Question

In the 6/52 lottery game, a player picks six numbers from 1 to 52. How many different choices does the player have if repetition is not allowed? Note that the order of the numbers is not important.

Answer 1

Answer:

The number of different choices the players have is 20,358,520.

Step-by-step explanation:

Combination can be used to solve this problem.

Combination is the selection of k objects from n distinct objects without replacement.

${n\choose k}=\frac{n!}{k!(n-k)!}$

The cards available are numbered from 1 to 52,i.e. there are total 52 cards.

A player has to select 6 cards from these 52 cards.

Compute the number of ways to select 6 cards from the 52 cards as follows:

${52\choose 6}=\frac{52!}{6!(52-6)!} =\frac{52!}{6!\times 46!} =\frac{52\times51\times50\times49\times48\times47\times46!}{6!\times46!}=20358520$

Thus, the number of different choices the players have is 20,358,520.

Answer 2

Answer: There are 20358520 ways to do so.

Step-by-step explanation:

Since we have given that

Numbers are written from 1 to 52

Numbers choose = 6

Since if repetition is not allowed.

We will use "combination":

Then the number of different ways to do so is given by

$C(52,6)=^{52}C_6=20358520$

Hence, there are 20358520 ways to do so.