Question

A bag contains 2 red balls, 4 blue balls and 8 green balls. Fatima draws 2 balls out of the bag. What is the probability that she gets a green ball and a blue ball?

Answer 1

factorial (!) means The result of multiplying a sequence of descending natural numbers down to 1 (such as 4 × 3 × 2 × 1)
The symbol is "!"

Examples:
4! = 4 × 3 × 2 × 1 = 24
7! = 7 × 6 × 5 × 4 × 3 × 2 × 1 = 5040

combination means : A collection of things, in which the order does not matter.

Example: For a fruit salad, how many different combinations of 2 ingredients can you make with apple, banana and cherry?
Answer: {apple, banana}, {apple, cherry} or {banana, cherry}

nCr = n!/r!(n-r)! (formula to find combinations)


n= total number, r the number of items we want to chose

QUESTION

total balls = 2+4+8 = 14 balls

fathima drawn 2 balls so the number of combination that can happen

14C2 = 14!/2!*(14-2)! = 14!/2!(12)! = 14*13*12!/2!*12! (14! = 14*13*12!)

14C2 = 14*13/2*1 = 91

now what way she want this to happen

8C1(one from green)* 4C1 (one from blue) * 2C0 (0 from red )

8C1 = 8 4C1 =4 2C0 =1

so it becomes 8*4*1 = 32

so propability = number of times desired outcome/total number of outcomes

so propability = 32/91