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Q:

# In how many different ways can 6 different balls be distributed to 4 different boxes, when each box can hold any number of ball?

 A) 2048 B) 1296 C) 4096 D) 576

Explanation:

Every ball can be distributed in 4 ways.

Hence the required number of ways = 4 x 4 x 4 x 4 x 4 x 4 = 4096

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

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.

2 22
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

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

7 127
Q:

In how many ways the letters of the word NUMERICAL can be arranged so that the consonants always occupy the even places ?

 A) 5! B) 6! C) 4! D) Can't determine

Answer & Explanation Answer: D) Can't determine

Explanation:

NUMERICAL has 9 positions in which 2, 4, 6, 8 are even positions.

And it contains 5 consonents i.e, N, M, R, C & L. Hence this cannot be done as 5 letters cannot be placed in 4 positions.

Therefore, Can't be determined.

5 112
Q:

36 identical books must be arranged in rows with the same number of books in each row. Each row must contain at least three books and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible ?

 A) 5 B) 6 C) 7 D) 8

Explanation:

The following arrangements satisfy all 3 conditions.

Arrangement 1: 3 books in a row; 12 rows.

Arrangement 2: 4 books in a row; 9 rows.
Arrangement 3: 6 books in a row; 6 rows.
Arrangement 4: 9 books in a row; 4 rows.
Arrangement 5: 12 books in a row; 3 rows.

Therefore, the possible arrangements are 5.

7 237
Q:

There are 11 True or False questions. How many ways can these be answered ?

 A) 11!/2 B) 1024 C) 11! D) 2048

Therefore, no. of ways of answering 11 questions = $\inline \fn_jvn 2^{11}$ = 2048 ways.