Two numbers are selected randomly from the set `S={1,2,3,4,5,6}` without replacement one by one. The probability that minimum of the two numbers is less than 4 is `1//15` b. `14//15` c. `1//5` d. `4//5`

Options

A. the smallest value of two is less than 3 is `13//28`
B. the bigger value of two is more than 5 is `9//14`
C. product of two number is even is `11//14`
D. none of these

Answer

A, B, C

Explanation

Here total number of cases is `.^(8)C_(2) = 28`
1. Number of favorable case is 13.
For 2 `rarr` 6 choices
For 1 `rarr` 7 choices
2. For 6 `rarr` 5 choices
For 7 `rarr` 6 choices
For 8 `rarr` 7 choices
3. For 1 `rarr` 4 choices (2, 4, 6, 8)
For 2 `rarr` 6 choices (3, 4, 5, 6, 7, 8)
For 3 `rarr` 3 choices (4, 6, 8)
For 4 `rarr` 4 choices (5, 6, 7, 8)
For 5 `rarr` 2 choices (6, 8)
For 6 `rarr` 2 choices (7, 8)
For 7 `rarr` 1 choice (8)
Alternate solution:
a. `(.^(8)C_(2) - .^(6)C_(2))/(.^(8)C_(2)) = (13)/(28)`
b. `(.^(8)C_(2)-.^(5)C_(2))/(.^(8)C_(2)) = (9)/(14)`
c. `(.^(8)C_(2) - .^(4)C_(2))/(.^(8)C_(2)) = (11)/(14)`