Using Combination formula,
Total 5,110 ways are possible that the coin land tails either exactly 9 times or exactly 2 times
Combinations:
If the order of events is not important, the concept of combination determines the number of ways in which a sequence of events can be obtained. I need to find the total number of expected events and the total number of possible events.
We have given that,
A unbiased or fair coin is tossed 15 times.
let us consider two events
A : the coin land tails exactly 9 times
B : the coin land tails exactly 2 times
Now, for calculating the required result we use
Combination formula,
ⁿCₓ= n! /x! (n-x)!
here, n= 15
the number of ways that exactly 9 times coin land as tails (n(A))= ¹⁵C₉ = 15! /9!× 6!
= 15×14×13×12×11×10×9!/ 9!(6×5×4×3×2×1)
= (15×14×13×12×11×10)/( 6×5×4×3×2×1 )
= (15×14×13×11)/6 = 7× 5× 13×11 = 5005
the number of ways that exactly 2 times coin land as tails (n(B))= ¹⁵C₂= 15! /2!× 13!
= 15×14×13!/13!(2)
= 15×14/2 = 15×7 = 105
Now, the number of ways that the coin land tails either exactly 9 times or exactly 2 times
= n(A) + n(B) = 5005 + 105
= 5110
Hence , total required ways are 5,110.
To learn more about Combination formula, refer:
https://brainly.com/question/295961
#SPJ4