Deloitte Permutations and Combinations Questions and Answers 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 18 English books so places needs to be is 19

And for the Hindi books 12 places are used ^{19}\textrm{C}_{12} = 50388 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!

 

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

^{5}\textrm{C}_{1}+^{5}\textrm{C}_{2}+^{5}\textrm{C}_{3}

= 5 +10+10

25 ways

Number of combination = ^{5}\textrm{C}_{3}   \times ^{4}\textrm{C}_{2} 

= 10 x 6

= 60

Here toys are identical and childrens are distinct.

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

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

 

Any factor  of 2^{4} \times 3^{7} \times 5^{2} which is a perfect square will be of the form 2^{x} \times 3^{y} \times 5^{z}   where

x can be 0,2,4(3 ways)

y can be 0,2,4,6(4 ways)

z can be 0,2(2 ways)

Required no of factors = 3\times 4\times 2

= 24

^{n}\textrm{C}_{7} = ^{n}\textrm{C}_{20}

=> n-7 =20

n = 27