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

Answer: 210

Step-by-step explanation:

choose 6 numbers out of 10:

₁₀C₆ = $\frac{10!}{(10-6)!(6)!}$

       = $\frac{10*9*8*7*6!}{(4)!(6)!}$

       = $\frac{10*9*8*7}{(4)!}$

       = $\frac{10*9*8*7}{4*3*2}$

       = 10 * 3 * 7

        = 210

Answer 2

Answer:

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

Step-by-step explanation: