# In the 6/54 lottery game, a player picks six numbers from 1 to 54. How many different choices...

## Question:

In the {eq}6\over 54 {/eq} lottery game, a player picks six numbers from {eq}1 {/eq} to {eq}54 {/eq}. How many different choices does the player have?

## Combinations:

$$\begin{align} ^nC_r = \dfrac{n!}{r!(n-r)!} \end{align} $$

This is the formula to calculate the number of possible ways for grouping or choosing, *r* items out of *n* different items available.

## Answer and Explanation:

Numbers are from 1 to 54. Hence total numbers are 54.

Numbers to be chosen = 6

The numbers can't be repeated, and the arrangement does not matter, only the grouping does. Hence, we will find the number of combinations possible.

Number of combinations possible are : {eq}^{54}C_6 = 25827165 ~ways {/eq}

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Combination: Definition, Formula & Examples

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Chapter 27 / Lesson 28
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