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Permutation and combination

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Topic starter

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

57 Answers


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.


It is 1. 100% probable. 



Sir,kindly post the Solution of  both the questions


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


In how many ways can you select exactly 7 letters from 3A, 4B, 2C and 1 D?


x+ y+ z=19, x≤ y≤ z, find total number of whole number solutions?


Find the number of ways to distribute 2n different balls into
(a) n equal lots
(b) equally among n children


Hello, Please solve :

How many different size rectangles are there in a square grid of 5 x 7 ?


Please solve:

how many words using all 8 letters of TATHAGAT can be formed such that 
a) no two Ts are together?
b) first letter is not T and last letter is not A?


 What should be the approach to solve the question in screenshot?


The collection of the questions are really great it will help me for my upcoming exams.

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