Permutation and com...

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# Permutation and combination

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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

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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.

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Sir,kindly post the Solution of  both the questions

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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.

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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

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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

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

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

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

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

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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?

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

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

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

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