Zoho Permutation & Combination Quiz 1

Solution

Possible Number of  hand shake = ^{450}\textrm{C}_{2} = 101025

Solution

In OBJECT there 6 letters 

Total number of possible words = 6! = 720 

Number of new words = 720 - 1 = 719

Solution:  

At unit’s  place possible digits = 5 

At ten’s  place possible digits =  4

At hundreds  place possible digits = 3 

At Thousand  place possible digits = 2 

At Tens of Thousands  place possible digits = 1

Possible Numbers = 5\times 4\times 3times 2\times 1 = 120

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Solution:  ^{9}\textrm{C}_{7} \times ^{5}\textrm{C}_{3} = 360 

For a rectangle, we need to select 2 parallel lines and the other two parallel lines that are perpendicular to each other. 

Hence,  ^{27}\textrm{C}_{2}\times ^{12}\textrm{C}_{2}  = 23166 rectangles

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Solution

captain can be selected in ^{35}\textrm{C}_{1} = 35

Vice - captain can be selected in  ^{34}\textrm{C}_{1} = 34

Total number of ways = 35 \times 34 = 1190

Solution

At unit’s  place no of  possible digits = 1 (only 5)

At ten’s  place no of  possible digits =  5

At hundreds  place no of possible digits = 5

At Thousand  place no of possible digits = 5 

Total no = 1 x 5 x 5 x 5 = 125

Solution

Total number of matches = ^{15}\textrm{C}_{2} = 105

 

In “MOTIHARI” M appears 1 time, R 1 time, O 1 time,  T 1 time,  H 1 time, A 1 time, I 2 times 

 

Possible words = \frac{8!}{1! \times 1! \times 1! \times 1! \times1! \times1!  \times 2!} = 20160  

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Solution  

At unit’s  place possible digits = 3 which is 2,6,8

At ten’s  place possible digits = 5 

At hundreds  place possible digits = 5 

 

Possible even Numbers = 5\times 5 \times 3 = 75