NTT Data Permutation and combination Quiz -1

No of Possible Arrangements = n! = 5! = 120

7! = 7 x 6 x 5 x 4 x 3 x 2 x1 = 5040

In MANGO there are 5 letters

Total number of possible words = 5! = 120

Number of new words = 120 - 1 = 119

^{7}\textrm{P}_{2} = \frac{7!}{(7-2)!} = \frac{7!}{5!} = 7 \times 6 = 42

In PAIN there is 4 letters

Number of possible arrangements = 4! = 4 x 3 x 2 x 1 = 24

 

In password hundreds place there can be zero

From A to Z 26 characters and 0 to 9 10 Characters

Total number of characters = 36

At unit’s  place possible digits = 36

At ten’s  place possible digits = 36

At hundreds  place possible digits = 36

Number of possible combinations = 36\times 36 \times 36

 

A 5x5 chessboard consists of 6 parallel horizontal lines and  6 parallel vertical lines.

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

Hence,  ^{6}\textrm{C}_{2}\times ^{6}\textrm{C}_{2}

= 225 rectangles

^{20}\textrm{C}_{2} = \frac{20!}{2! \times 18!} = 190

Captain can be selected in ^{5}\textrm{C}_{1} = 5

Vice - Captain can be selected in  ^{4}\textrm{C}_{1} = 4

Total number of ways of Selection  = 5 \times 4 = 20

^{15}\textrm{C}_{3} = \frac{15!}{3! \times 12!} = 455