TCS NQT Permutation and Combinations Questions Quiz 1

Single digit number plates =   ⁵C₁ x 1!
Two digit number plates =   ⁵C₂ x 2!
Three digit number plates =   ⁵C₃ x 3!
Four digit number plates =   ⁵C₄ x 4!
Five digit number plates =   ⁵C₅ x 5!
Total = (⁵C₁ x 1!) + (⁵C₂ x 2!) + (⁵C₃ x 3!) + (⁵C₄ x 4!) + (⁵C₅ x 5!) = 5 + 20 + 60 + 120 + 120 = 325

 

18!*2

References :

1. Circular Permutations Formula


2. How to solve Circular Permutations


3. Tips and Tricks to solve Circular Permutations

• Consider 1 man along with two sisters as one group.. so 18 objects, they can be arranged in 17! ways as circular. (Formula for Circular Permutation is : (n - 1)!


• The one man in between the two sisters can be out of any 18 men so, 17!*18..


• The two sisters can be arranged in 2 ways so 18!*2

• No.of alphabets=26 (a-z), no.of digits=10(0-9).


• Ways of arranging two alphabets with out repetition=26*25;


• Ways of forming two digits without repetition=10*9

Following would possible scenarios: Men - (0, 1, 2, 3)

If there are 0 men, then 11 women. Similarly, if there are 1 men then there would be 10 women so on ...

• Ways of choosing (0 Men, 11 Women) : (⁵C₀ × ¹¹C₁₁)


• Ways of choosing (1 Men, 10 Women) : (⁵C₁ × ¹¹C₁₀)


• Ways of choosing (2 Men, 9 Women) : (⁵C₂ × ¹¹C₉)


• Ways of choosing (3 Men, 8 Women) : (⁵C₃ × ¹¹C₈)

a,b,c,d are grouped ie consider them as one and remaining as 6.
total 6+1=7! ways

To form a triangle we need 3 points

• Select 2 points from the 10 points of line AB & 1 from the 8 on AC = (¹⁰C₂)*(⁸C₁)


• Select 2 points from the 8 points of line AC & 1 from the 10 on AB= ⁸C₂)*(¹⁰C₁

Ans is 575

• One digit no = 4 (0 is not a positive integer)


• Two digit no=4 * 5 = 20


• Three digit no=4 * 5 * 5 = 100
  
  
  
  • Four digit no=3 * 5 * 5 * 5 = 375(the possibility for 1,2,3 will come in the first position)
  
  
  • Four digit no=1 * 3 * 5 * 5 (the possibility of 4 is fixed in the first position and then 0,1,2 is comes in second position)
  
  
  
  


• And the last digit is 4300 we include this number also

Since we have to form 6 digit even numbers can be formed from digits 1 to 7.

To form even numbers, the units digit should be either 2,4 or 6. Therefore, there are three ways.

Now, since the second last digit is also even. Since, from the three numbers, one of the numbers is used in the units place. Therefore, there are 2 ways for the second last digit, as the digits should not repeat.

Now, 5 numbers are left. There are 5! ways to fill the remaining digits.

Therefore, Total numbers formed = 5! * 3 * 2

= 720 ways.

Therefore, 720, six-digit even numbers can be formed.