## Solution
We have 3 scenarios here:
1) 1 tech2 businessmen: 4C1 x 8C2 = 112
2) 2 tech1 businessman: 4C2 x 8C1 = 48
3) 3 tech0 businessmen: 4C3 = 4
Total: 112+48+4 = 164
## What the question and answer could be
An entrepreneurship competition requires registering teams to have 3 team members, at least one of which must be a technology co-founder. If all team members must come from the auditorium during the meet and greet event which has 4 technologists and 8 businessmen, how many possible team submissions are possible?
Options:
(A) 76
(B) 100
(C) 164
(D) 198
(E) 202
(C)

## Solution
The probability of selecting girl is: 25/100 = 1/4
The probability of selecting rich is: 20/100 = 1/5
The probability of selecting fair complexioned is: 10/100 = 1/10
Three are independent;probability of rich and fair complexioned girl is:
(1/4) (1/5) (1/10) = 1/200
## What the question and answer could be
A class consists of 100 students, 25 of them are girls and 75 boys; 20 of them are rich and remaining poor; 10 of them are fair complexioned. The probability of selecting a fair complexioned rich girl is
Options:
(A) 1/200
(B) 1/59
(C) 1/56
(D) 1/54
(E) 1/53
(A)

## Solution
Answer = E = 4
If least = -4, then largest = 5
Range = 5 - 1 = 4
## What the question and answer could be
List K consists of 10 consecutive integers. If -4 is the least integer in list K, what is the range of the positive integers in list K?
Options:
(A) 5
(B) 6
(C) 7
(D) 11
(E) 4
(E)

## Solution
Division of m+n+p objects into three groups is given by (m+n+p)!m!n!p!(m+n+p)!m!n!p!
But 7 = 1 + 3 + 3 or 1 + 2 + 4 or 1 + 1 + 5
So The number of ways are (7)!1!3!3!12!(7)!1!3!3!12! + (7)!1!2!4!(7)!1!2!4! + (7)!1!1!5!12!(7)!1!1!5!12! = 70 + 105 + 21 = 196
## What the question and answer could be
Seven different objects must be divided among three persons. In how many ways this can be done if at least one of them gets exactly one object.
Options:
(A) 223
(B) 776
(C) 287
(D) 196
(E) 211
(D)