4
Q:

A Committee of 5 persons is to be formed from a group of 6 gentlemen and 4 ladies. In how many ways can this be done if the committee is to be included atleast one lady?

A) 123 B) 113
C) 246 D) 945

Answer:   C) 246



Explanation:

A Committee of 5 persons is to be formed from 6 gentlemen and 4 ladies by taking.

(i) 1 lady out of 4 and 4 gentlemen out of 6

(ii) 2 ladies out of 4 and 3 gentlemen out of 6

(iii) 3 ladies out of 4 and 2 gentlemen out of 6

(iv) 4 ladies out of 4 and 1 gentlemen out of 6

In case I the number of ways =  = 4 x 15 = 60

In case II the number of ways =  = 6 x 20 = 120

In case III the number of ways =  = 4 x 15 = 60

In case IV the number of ways =  = 1 x 6 = 6

Hence, the required number of ways = 60 + 120 + 60 + 6 = 246

Q:

A,B,C,D,E,F,G and H are sitting around a circular table facing the centre but not necessarily in the same order. G sits third to the right of C. E is second to the right of G and 4th to the right of H. B is fourth to the right of C. D is not an immediate neighbour of E. A and C are immediate neighbours.

 Which of the following is/are correct ?

A) F is third to the left of B B) F is second to the right of B
C) B is an immediate neighbour of D D) All of the above
 
Answer & Explanation Answer: B) F is second to the right of B

Explanation:

From the given information, the circular arrangement is

EXP.

Here F is second to the right of B and the remaning all are wrong.

Report Error

View Answer Workspace Report Error Discuss

2 7
Q:

Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?

A) 43929 B) 59049
C) 15120 D) 0
 
Answer & Explanation Answer: A) 43929

Explanation:

Number of words with 5 letters from given 9 alphabets formed =

Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is = 

Number of words can be formed which have at least one letter repeated =  -  

= 59049 - 15120

= 43929

Report Error

View Answer Workspace Report Error Discuss

6 75
Q:

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

A) 5040 B) 3650
C) 4150 D) 2520
 
Answer & Explanation Answer: D) 2520

Explanation:

Total number of letters in the word ABYSMAL are 7

Number of ways these 7 letters can be arranged are 7! ways

But the letter is repeated and this can be arranged in 2! ways

=> Total number of ways arranging ABYSMAL = 7!/2! = 5040/2 = 2520 ways.

Report Error

View Answer Workspace Report Error Discuss

8 178
Q:

In how many ways the letters of the word OLIVER be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right ?

A) 186 B) 144
C) 136 D) 120
 
Answer & Explanation Answer: D) 120

Explanation:

In given word OLIVER there are 3 vowels E, I & O. These can be arranged in only one way as dictionary order E, I & O.

There are 6 letters in thegiven word.

First arrange 3 vowels.

This can be done in 6C3 ways and that too in only one way.(dictionary order E, I & O)

Remaining 3 letters can be placed in 3 places = 3! ways

Total number of possible ways of arranging letters of OLIVER = 3! x 6C3 ways

= 6x5x4 = 120 ways.

Report Error

View Answer Workspace Report Error Discuss

7 242
Q:

Find the total numbers greater than 4000 that can be formed with digits 2, 3, 4, 5, 6 no digit being repeated in any number ?

A) 120 B) 256
C) 192 D) 244
 
Answer & Explanation Answer: C) 192

Explanation:

We are having with digits 2, 3, 4, 5 & 6 and numbers greater than 4000 are to be formed, no digit is repeated.

The number can be 4 digited but greater than 4000 or 5 digited.

Number of 4 digited numbers greater than 4000 are
4 or 5 or 6 can occupy thousand place => 3 x 4P3 = 3 x 24 = 72.

5 digited numbers = 5P5 = 5! = 120

So the total numbers greater than 4000 = 72 + 120 = 192

Report Error

View Answer Workspace Report Error Discuss

9 240