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  • In a lottery game, you need to select 3 numbers from a pool of 15 . How many different combinations of numbers are possible?  Option: 1 4

In a lottery game, you need to select 3 numbers from a pool of 15 . How many different combinations of numbers are possible?
 

Option: 1

455


Option: 2

896


Option: 3

520


Option: 4

555


Answers (1)

best_answer

To calculate the number of different combinations of 3 numbers that can be selected from a pool of
15, we can use the formula for combinations:

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

In this case, n = 15 (the total number of numbers in the pool) and r = 3 (the number of numbers to
be selected). Plugging these values into the formula, we get:

\begin{aligned} \mathrm{C}(15,3)&=\frac{15 !}{(3 !(15-3) !) } \\ & =\frac{15 !}{(3 ! 12 !) }\\ & =\frac{(15 \times 14 \times 13) }{(3 \times 2 \times 1)} \\ & =455 \end{aligned}

Therefore, there are 455 different combinations of 3 numbers that can be selected from a pool of 15
in the lottery game.

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Anam Khan

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