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 27 English books so places needs to be is 28

And for the Hindi books 26 places are used

^{28}\textrm{C}_{26}

= 378 ways

Total number of combination  is 10^{10}

:  triangle needs 3 points

^{14}\textrm{C}_{3} – ^{7}\textrm{C}_{3}

= 329

no of ways = ^{12}\textrm{C}_{3}

 

: 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!

Now books set of 4 books can be arranged in total of 4! ways

Total no of ways = 9! \times 4!

 

Number of possible ways of selection =

^{15}\textrm{C}_{4} =1365

 

Here toys are identical and childrens are distinct.

Required numner of ways = ^{20-1}\textrm{C}_{10-1}

= ^{19}\textrm{C}_{9}

 

we assume all the vowels to be a single character, i.e., “IE” is a single character.
So, now we have a total of 5 characters in the word, namely, D, R, V, R, IE.
But, R occurs 2 times.
=> Number of possible arrangements = 5! / 2! = 60
Now, the two vowels can be arranged in 2! = 2 ways.
=> Total number of possible words such that the vowels are always together = 60 x 2 = 120
Also, total number of possible words = 6! / 2! = 720 / 2 = 360
Therefore, total number of possible words such that the vowels are never together = 360 – 120 = 240

5 different colours and 3 varieties

=5^{3}

=125