Hi. I have an answer for this question however, not sure. In a certain lottery, 4 numbers between 1 and 10 inclusive are drawn. These are the winning numbers. How many different selections are possible? Assume that the order in which the numbers are drawn are not imprt. (10*9*8*7)/(1*2*3*4)=210.4! = 4*3*2*1= with 24 as the final answer??

You are choosing 4 from 10 or C(10,4) = 210

(why are you multiplying 210 by 4! ?
then the order would be important. )

Hello! It seems like you're trying to find out how many different selections are possible in a certain lottery where 4 numbers between 1 and 10 inclusive are drawn, and the order in which the numbers are drawn does not matter.

To calculate the number of different selections, you can use the concept of combinations. Since the order doesn't matter, we need to find the number of combinations of 4 numbers chosen from a set of 10 numbers.

The formula for combinations is given by:

C(n, r) = n! / (r!(n-r)!),

where n is the total number of objects to choose from, and r is the number of objects to be chosen.

In this case, n = 10 (as there are 10 numbers to choose from) and r = 4 (as we need to choose 4 numbers).

Plugging in the values, we have:

C(10, 4) = 10! / (4!(10-4)!)
= 10! / (4! * 6!)

Now, let's calculate the factorials involved:

10! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
4! = 4 * 3 * 2 * 1
6! = 6 * 5 * 4 * 3 * 2 *1

Simplifying the expression further:

C(10, 4) = (10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1) / ((4 * 3 * 2 * 1) * (6 * 5 * 4 * 3 * 2 *1))

Now, let's cancel out the common factors:

C(10, 4) = (10 * 9 * 8 * 7) / (4 * 3 * 2 * 1)

Calculating the value:

C(10, 4) = 210

So, there are 210 different selections possible in this lottery.

Your calculation of (10*9*8*7)/(1*2*3*4) is correct, but the value of (10*9*8*7) is already equal to 5040, and not 210. Therefore, the correct answer is 210, not 24.