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Permutations & Combinations

Important Instructions
51.

From a group of 7 men and 6 women, five persons are to be selected to form a committee so that at least 3 men are there on the committee. In how many ways can it be done?

Answer: D

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52.

In how many ways can the letters of the word INDIA be arranged, such that all vowels are never together?

Answer: B

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53.

There are 20 points in a plane, how many triangles can be formed by these points if 5 are colinear?

Answer: A

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54.

A person ordered 5 pairs of black socks and some pairs of brown socks. The price of a black pair was thrice that of a brown pair while preparing the bill the bill clerk inter-changed the number of black and brown pairs by mistake which increased the bill by 100% what was the number of pair of brown socks in the original order?

Answer: D

Let the bought x pairs of brown socks and the price of each brown pair be Y. 

Then total cost = 5x3Y+xy 

Changed cost = 5xY+x*3Y 

According to the question . 

5y+3xy –(15y+xy)/15y+xy x 100% = 100% 

=> 5y+3xy-15y-xy/ 15y+xy x100% = 100% 

=> 5y+3xy = 15y+xy+15y+xy 

=> 5y+3xy = 30y+2xy 

=> xy= 25y 

=> x=25. 

Hence the original pair of brown socks = 25.

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55.

In a society, it is customary for friends of the same sex to hug and for friends of opposite sex to shake hands when they meet. A group of friends met in a party and there were 24 hand shakers. Which one among the following numbers indicates the possible number of hugs?

Answer: C

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56.

Out of 7 consonants and 4 vowels, how many words of 3 consonants and 2 vowels can be formed?

Answer: C

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57.

A bank has 6 digit account number with no repetition of digits within a account number. The first and last digit of the account numbers is fixed to be 4 and 7. How many such account numbers are possible?

Answer: D

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58.

Twelve people from a club, by picking lots. One of them will host a dinner for all once in a month. The number of dinners a particular member has to host in one year is

Answer: D

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59.

In how many ways can the letters of the word 'LEADER' be arranged?

Answer: C

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60.

A letter lock consists of three rings each marked with six different letters. The number of distinct unsuccessful attempts to open the lock is at the most -.

Answer: C

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