Fundamental Principle of Counting

Q. Number of ways in which 12 different balls can be divided into groups of 5, 4 and 3 balls are

1. $\frac{12!}{5!4!3!}$
2. $\frac{12!}{5!4!3!3!}$
3. None of these
4. $\frac{12!}{5!4!}$

Q. How many numbers greater than a million can be formed with the digits 5, 5, 2, 2, 1, 7, 0?

1. 980
2. 920
3. 1200
4. 1080

Q. How many 7 digit numbers can be formed using the digits 1, 2, 0, 2, 4, 2, 4?

1. 360
2. 240
3. 120
4. 424

Q. The number of words that can be formd out of the letters of the word COMMITTEE is

1. $\frac{9!}{(2!{)}^3}$
2. $9!$
3. $\frac{9!}{(2!{)}^2}$
4. $\frac{9!}{2!}$

Q. In the figure given below, the lines represent one way roads allowing travel only northwards or only eastwards. Along how many distinct routes can a car reach point A from point B?

1. 56
2. 66
3. 76
4. 46

Q. There are 5 different caps $c_1,c_2,c_3,c_{4}and{c}_5$ and 5 different boxes $B_1,B_2,B_3,B_{4}and{B}_5$. The capacity of each box is sufficient to accomodate all the 5 caps.

If $C_{1}and{C}_5$ are similar in all aspects, in how many ways can you arrange the caps in such a way that all the boxes have one cap?

1. 70
2. 60
3. 75
4. 80

Q. In how many ways can the letters of the word ASSASSINATION be arranged?

1. 181800
2. 108108
3. 10810800
4. 818100

Q. There are 5 different caps $c_1,c_2,c_3,c_{4}and{c}_5$ and 5 different boxes $B_1,B_2,B_3,B_{4}and{B}_5$. The capacity of each box is sufficient to accommodate all the 5 caps. If $B_1$ and $B_5$ have the caps $C_1$ and $C_5$ among themselves, in how many ways can you arrange the caps among the 5 boxes?

1. 400
2. 485
3. 500
4. 365

Q. A set of 6 questions contains true/false type questions. Maximum how many students can take the test if all the students answer differently from others and must attempt all the questions?

1. 32
2. 128
3. 256
4. 64

Q. If you have 3 jeans and 5 trousers, in how many ways can you wear either a jeans or a trouser?

1. 5
2. 8
3. 30
4. 15