An unbiased die is thrown 6 times. Calculate the probabilities that the six scores obtained will

i) be 1, 2,3, 4, 5,6 in some order

ii) have a product which is an even number

iii) consists of exactly two 6’s and four odd numbers

**Solution**

iii Alternative solution

6C2: 6 slots choose 2 slots to insert the two 6s. Remaining 4 slots automatically will be for the four odd numbers.

3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4

3^4: Each odd number has 3 choices. for 4 odd numbers will be 3^4

Probability = (6C2 x 3^4) / 6^6 = 5/192