Question

From a group of 11 people, you randomly select 3 of them.

What is the probability that they are the 3 oldest people in the group?

Give your answer as a decimal rounded to 4 decimals

Answer 1

Step 1. There are 11 People in the group and we have to select 3 of them. So, there are ¹¹C₃ groups possible.

¹¹C₃ = 11 ! / { 3! x (11-3)! } .......... Formula: ⁿC_r = n ! / { r! x (n-r)! }

= 11 ! / { 3! x 8! }

= 8! x 9 x 10 x 11 / { 3 x 2 x 1  x 8! } ........... 11 ! = 8! x 9 x 10 x 11

= (9 x 10 x 11) / ( 3 x 2)

= 165

Step 2. There is only 1 group of the 3 oldest people is possible out of 165 groups.

Step 3. So,

P (group with 3 oldest people) = No. of Favourable Outcomes / No. of total outcomes

= 1/ 165

= 0.0061