1. Number of selections of atleast 10 articles from 19 different articles is.

A) 2^19 B) 2^18 C) 2^19 - 1 D) 2^18 - 1 E) None

3 points are randomly selected on a sphere,what is the probability that all of them lie in the same hemisphere?

Should it not be?-2πrsq./4πrsq.

No!

It is 1. 100% probable.

An institute has 5 departments and each department has 50 students. If students are picked up randomly from all 5 departments to form a committee, what should be the minimum number of students in the committee so that at least one department should have representation of minimum 5 students?

1. 11

2. 15

3. 21

4. 41

5. None of the above

The maximum number of students can be picked from each department such that 5 students are not selected from the same department is 4.

Therefore, after 4 students from each department are selected i.e 4 x 5 = 20 , the 21st student selected will be the fifth student to be selected from one of the 5 departments.

Hence, , 20+1 = 21 students should be selected in total to ensure that at least five students from one of the departments is selected.

In how many ways can we select 3 numbers from first 20 positive integers, such that their product is always divisible by 5?

Sir, won't the answer be 580?

yes 580 is the correct answer .

Approach : 1

select 3 numbers in 20C3 ways.

cases when none of the selected number is a multiple of 5 : 16C3 ways

20C3 - 16C3 = 580

Approach : 2

4C1 x 16C2 + 4C2 x 16C1 + 4C3 = 580

How many 3-letter words can be formed using the letters of the word 'INSTITUTE'?

case 1 - when all letters are distinct

then there are 6 different letters hence 6P3 = 120

Case 2 - when 1 letter repeated twice

then it can be either I or T means 2C1 cases and 1 more letter means 4C1 case

further arrangements 3! , hence total 2C1*4C1*3! = 48

Case 3 - when all letters are same , that is only one case TTT

hence total 169 cases