Question

Use the Counting Principle to find the probability of choosing the 6 winning lottery numbers when the numbers are chosen at random from 0 to 9.

Answer 1

How many ways can 6 numbers be chosen from 10?

combinations = n! / r! *(n-r)!

combinations = 10! / (6! * 4!)

combinations = 10 * 9 * 8 * 7 * 6! / (6! * 4!)

combinations = 10 * 9 * 8 * 7 / 4 * 3 * 2* 1

combinations = 10 * 3 * 7

combinations = 210

So the probability is 1 / 210 or 0.0047619048

Explanation:

Answer 2

Answer: 210

Explanation:

choose 6 numbers out of 10:

₁₀C₆ =
`(10!)/((10-6)!(6)!)`

=
`(10*9*8*7*6!)/((4)!(6)!)`

=
`(10*9*8*7)/((4)!)`

=
`(10*9*8*7)/(4*3*2)`

= 10 * 3 * 7

= 210