Adie is rolled 20 times. given that three of the rolls came up 1, five came up 2, four came up 3, two came up 4, three came up 5, and three came up 6, how many different arrangements of the outcomes are there

Solution:

Number of times a die is rolled = 20

1 - 3=A

2 - 5=B

3 - 4=C

4 - 2=D

5 - 3=E

6 -  3=F

Total number of arrangements of outcomes , when a dice is rolled 20 times given that 1 appear 3 times, 2 appears 5 times, 3 appear 4 times, 4 appear 2 times , 5 appear three times, and 6 appear 3 times

            = Arrangement of 6 numbers (A,B,C,D,E,F) in 6! ways and then arranging outcomes

= 6! × [ 3! × 5! × 4!×2!×3!×3!]

= 720 × 6×120×24×72→→[Keep in Mind →n!= n (n-1)(n-2)(n-3)1]

= 895795200  Ways

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.