Use the formula for nCr to solve Exercises 49–56.

To win at LOTT...

Question

Use the formula for nCr to solve Exercises 49–56.

To win at LOTTO in the state of Florida, one must correctly select 6 numbers from a collection of 53 numbers (1 through 53). The order in which the selection is made does not matter. How many different selections are possible?

Accepted Answer

Hey everyone here we are asked to find how many groups of eight students are possible in a 50 student class. So our first step here we need to recall the combination formula which is N. C. R. Is equal to and factorial divided by the quantity of n minus R. Factorial times R factorial. So in words this formula is the total possible combinations of our items taken from n items. So in this case the end items are the total. So we have a total of 50 students and then are are the number of students in a group. So we have eight. And now with this we can just plug in these values into our formula. So we have 50 C. Eight is equal to n. Factorial which is 50. So we have 50 factorial in the numerator divided by in the denominator we have any minus R. So we have 50 minus eight factorial times R factorial or eight factorial. And now we can just do some quick simplifications. So in the numerator we still have 50 factorial. And in the denominator we have 50 minus eight giving us 42 factorial times eight factorial. And now with this we can just evaluate this this Expression here in our calculators and it gives us a total possible number of combinations of 536,878, which is our answer here for choice. A thanks for watching, I hope you found this video helpful and I'll see you again next time