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  • In a lottery game, you need to select 6 numbers from a pool of 40 . How many different combinations of numbers are possible if one specific number must be included?  <div class='

In a lottery game, you need to select 6 numbers from a pool of 40 . How many different combinations of numbers are possible if one specific number must be included?

 

Option: 1

452523


Option: 2

848961


Option: 3

575757


Option: 4

121000


Answers (1)

best_answer

If one specific number must be included in the selection of 6 numbers from a pool of 40 in a lottery game, we can treat it as selecting the remaining 5 numbers from a pool of 39 .

To calculate the number of different combinations, we can use the formula for combinations:

\mathrm{C(n, r)=\frac{n !}{(r !(n-r) !)} }

In this case, n=39 (since one number is fixed and we select the remaining 5 from a pool of 39 ) and r =5 (the number of numbers to be selected).
Plugging these values into the formula, we get:

\begin{aligned} \mathrm{C}(39,5)&=\frac{39 !}{(5 !(39-5) !) }\\ & =\frac{39 !}{(5 ! 34 !) }\\ & =\frac{(39 \times 38 \times 37 \times 36 \times 35)}{(5 \times 4 \times 3 \times 2 \times 1) }\\ & =575,757 \end{aligned}

Therefore, there are 575,757 different combinations of 6 numbers, including one specific number, that can be selected from a pool of 40 in the lottery game.

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