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  • In a lottery game, you need to select 5 numbers from a pool of 35 . How many different combinations of numbers are possible?  Option: 1 <

In a lottery game, you need to select 5 numbers from a pool of 35 . How many different combinations of numbers are possible?

 

Option: 1

29652


Option: 2

84896


Option: 3

35960


Option: 4

12650


Answers (1)

best_answer

To calculate the number of different combinations of 5 numbers that can be selected from a pool of 35, we can use the formula for combinations:

\mathrm{C(n, r)=\frac{n ! }{(r !(n-r) !)} }
In this case, n=35 (the total number of numbers in the pool) and r=5 (the number of numbers to be selected). Plugging these values into the formula, we get:

\begin{aligned} \mathrm{C}(35,5)&=\frac{35 !}{(5 !(35-5) !)} \\ & =\frac{35 !}{(5 ! 30 !)} \\ & =\frac{(35 \times 34 \times 33 \times 32 \times 31)}{(5 \times 4 \times 3 \times 2 \times 1)} \\ & =35,960 \end{aligned}
Therefore, there are 35,960 different combinations of 5 numbers that can be selected from a pool of 35 in the lottery game.

Posted by

Kuldeep Maurya

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