Quiz-1

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

E X E X E X E ………. X E

There are 18 Hindi books, so places needs to be is 19

And for the English books 12 places are used ¹⁹C₁₂ = 50388 ways

Distinct functions are the one you cannot repeat.

So, Without repetition, total numbers = 10^{10}

Since, any triangle needs 3 points

∴ Number of triangles that can be formed = 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

Since, 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)!  = 8!

Now books can be arranged in total of 4 ways = (9-1)! × 4!

Now books can be placed in any direction (from either of the side)

∴ Number of ways = \frac{(9-1)!\times 4!}{2}=483840

The number of ways in which he 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) × (M+1)………………….. upto N   = (M+1)ⁿ

Number of different ways of selection are = (M+1)ⁿ - 1

Let there be students from 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 = ⁸C₅ײC₁

Hence, total ways = ⁸C₆ + ⁸C₅ײC₁        =  728 ways

They can have different colors in 5^{3} = 125

Number of ways of selecting 3 consonants from 7 = ⁷C₃
Number of ways of selecting 2 vowels from 4 = ⁴C₂
Number of ways of selecting 3 consonants from 7 and 2 vowels from 4 =  ⁷C₃×⁴C₂ = 210

It means we can have 210 groups where each group contains total 5 letters (3 consonants and 2 vowels).
Number of ways of arranging 5 letters among themselves = 5! = 720

Hence, number of ways = 210×120 = 25200