Permutation and Combinations Quiz-1

In order that no two Hindi come together we need to have following arrangement.

X E X E X E X……….E X

There are 28 English books if we placed alternatively. so we have 28 places there for place Hindi and the will never be together.

And for the Hindi books 26 places are used ²⁸ c ₂₆ = 378 ways

Domain : A : {1, 2, 3, 4, …..10}

Codomain : B : {1, 2, 3, 4, …..10}

= 10 * 10 …..10

= 10¹⁰

Total number of distinct functions = 10¹⁰

Triangle needs 3 points

¹⁴c₃ – ⁷c₃

= 329

Let the total number of persons be N.
Given, total number of hand-shakes is 66
For a hand shake we require two people, total number of handshake is NC2
NC2 = 91
N(N – 1) / 2 = 91
N(N-1) = 182

N(N-1) = 14*13

N = 14.

: the 4 books to be together can be treated as 0ne set

So we have 1 set of books and remaining 8 books which makes total 9 books to be placed in shelf

(9-1)!

Now books can be arranged in total of 4 ways

(9-1)! * 4!

Now books can be placed in any direction so

(9-1)! * 4! /2

483, 840

: the number of ways in which a visitor can visit the places are

5c1 + 5c2+ 5c3= 5 +10+10

25 ways

there are M keys which can be used in N ways

Number of ways to select the M keys are M+1

Total ways are (M+1) X(M+1)…………………..N

(M+1)n

Number of different ways of selection are

(M+1)n  - 1

let there be students A to j out of which A and b don’t participate together,

Case 1: neither of A and B come then the remain students’ needs to be selected 8c6

Case 2: only one of them comes i.e. selecting 5 out of 8 and one from A and b

8c6 + 8c5 x 2c1

=168 ways

Explanation :

We can have 5 colours for 3 styles in 5³ = 125 ways

= 125

Answer : The candidate will fail if he fails either in 1 or 2 or 3 or 4 or 5 Question, ∴ Required number of ways ⁵C₁ + ⁵C₂ + ⁵C₃ + ⁵C₄ + ⁵C₅ = 31