Permutation and Combination Quiz-1

^{60}\textrm{C}_{2} = \frac{60\times 59}{2} = 1770

none

Ways of selection = ^{12 + 16 +14}\textrm{C}_{2} = ^{42}\textrm{C}_{2} =  21\times 41 = 861

Ways of arrangement around a circular table = (n-1)! = (15-1)! = 14!

No of letters in SHIFT = 5

No of ways = 5! = 120

A Triangle can be formed by joining three non- collinear points

So no of Triangle = ^{13}\textrm{C}_{3} = 286

Required no of line segments =  ^{7}\textrm{C}_{2} = 21

^{9}\textrm{C}_{4} \times ^{7}\textrm{C}_{3} = 126 \times 35 = 4410

At unit’s place possible digits = 5

At ten’s  place possible digits = 5

At hundreds  place possible digits = 5

At Thousand  place possible digits = 5

Total possible numbers = 5 x 5 x 5 x 5 = 625

No of letters in “CAPSLOCK” = 8

When CK remains together then “CK” taken as 1 letter but they can change their position among themselves

Possible arrangements =  7! Times 2! = 10080[/latex

At unit’s place possible digits = 3 which is (9,7,5)

At ten’s place possible digits = 5

Total possible numbers = 3 x 5 = 15