Permutations and Combinations Test - 1

We have a regular tetrahedron has 4 faces and we have to colour it with 4 different colours in 4!=24 ways.

But in this we will be getting many overcountings .

We have there are 12 ways in which we can orient a regular tetrahedron  

Hence the number of distinct ways of colouring a regular tetrahedron  with 4 different colours is 24/12=2

A team of 4 players are to be selected.

2 out of 6 men can be done in ⁶C₂ ways. 2 out of 4 women can be done in ⁴C₂ways. 

So the number of ways to select 4 players is ⁶C₂x ⁴C₂= 90.

Now we can arrange these people to form  mixed doubles.

 If M₁,M₂,W₁,W₂, are the 4 members selected then one team can be chosen as (M₁,W₁)or(M₁,W₂)  in 2 different ways 

Therefore the required number of arrangements= 90x2 = 180.

Number of ways of forming 5 digit numbers= 5×4×3×2×1=120

 Number of ways of forming 4 digit numbers= 5×4×3×2=120

Number of ways of forming 3 digit numbers= 5×4×3=60

Number of ways of forming 2 digit numbers=5×4=20

number of ways of forming 1 digit numbers= 5

Hence the total number of ways = 120+ 120 + 60+ 20+ 5 = 325

• .Arrange all the alphabets in alphabetical order ( E, F , I  , W )
•  4 alphabets can form 4! words = 24 words.

You have two different kinds of such three-digit even numbers.First is  5 at the hundred'splace and  second 5 is not at the hundred'splace

•  In first case no is of the form 57x, where x is the unit's digit ,which can  be 0,2,4,6,8 which is just 5 possibilities.Hence the no of possibilities in this case is 1x1x5=5
• In second case the hundred's digit can be 1,2,3,,4,,6,7,8,or,9 which is 8 ways and the ten's digit  can be  any of the 9 numbers and unit digit can be any of the 5 even numbers .Therfore the no: of ways  will be 8×9×5=360

So total we  have 360 + 5 = 365 possibilities.