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 so places needs to be is 19

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

distinct functions you cannot repeat.
So 10¹⁰

Triangle needs 3 points

¹⁴c₃ – ⁷c₃

= 329

There are 3 alternatives to answer the question

So the option can be 312

On one of the option we have that we didn’t answer the question at all

312  - 1

: 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 : Option 2
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