# Fundamental Principle of Counting

## Trending Questions

**Q.**How many numbers can be formed from 1, 2, 3, 4, 5 (without repeating), where the digit at the unit’s place must be greater than that in the ten’s place?(CAT 1998)

- 2×4!
- 54
- 60

**Q.**A man has 9 friends: 4 boys and 5 girls. In how many ways can he invite them, if there have to be exactly 3 girls in the invitees? (CAT 1996)

- 80
- 200
- 320
- 160

**Q.**

$12$ persons are to be arranged at a round table . If two particular persons among them are not to be side by side, the total number of arrangements is?

$9(10!)$

$2(10!)$

$45(8!)$

$10!$

**Q.**

How many numbers greater than a hundred and divisible by $5$can be made from the digits $3,4,5,6,$ if no digit is repeated?

$6$

$12$

$24$

$30$

**Q.**

Find the largest four-digit number divisible by $16$.

**Q.**

What is the place value of $6$ in $64$?

$6$

$60$

$64$

$10$

**Q.**In how many ways can 10 people line up at a ticket window of a cinema hall?

- 3482800
- 3328800
- 3628800
- 344800
- None of these

**Q.**

In how many of the distinct permutations of the letters in “MISSISSIPPI” do the four I’s not come together?

**Q.**In which year was the difference between the basic model and the premium model of cars produced by company E the second highest?

- 2008
- 2009
- 2010
- 2006
- 2007

**Q.**A basket has 5 oranges and 4 apples. In how many ways can you make a selection if you have to take at least 1 orange and 1 apple?

- 465
- 20
- 345
- 365
- 22

**Q.**Out of 6 green balls, 4 blue balls, in how many ways can we select one or more balls ?

- 42
- 34
- 31
- 22
- None of these

**Q.**How many numbers greater than a million can be formed with the digits 2, 3, 0, 3, 4, 2, 3?

**Q.**

There are $5$ways leading to a town from a village. the number of different ways in which a villager can go to the town and return back is

$20$

$25$

$5$

$10$

**Q.**How many seven letter words can be formed without repetition out of the letters of the word ′MISTAKE′ such that the vowels go only into the odd places

- 786
- 480
- 625
- 576

**Q.**

It was a sunday on 9th Nov, 2006. What day of the week was it on 9th Nov, 2005?

Sunday

Thursday

Friday

Saturday

Tuesday

**Q.**

If farmer Q sells 14 kg of wheat, farmer S sells 21 kg of jowar and farmer R sells 30 kgs of sugarcane, what will be their combined earning?

Rs. 779

Rs. 650

Rs. 786

Rs. 699

None of these

**Q.**

On 23rd Apr, 2001 it was Monday. What was the day of the week on 23rd Apr, 2000?

Tuesday

Monday

Thursday

Sunday

**Q.**For numbering the pages of an encyclopedia the printer used 2989 digits. How many pages did the book contain?

- 924
- 996
- 1024
- 1009

**Q.**Find the digits at the tens place of 624.

- 3
- 1
- 9
- 5

**Q.**What is the difference between the number of CDs produced by Company B and the number of Computers produced by Company A?

- 200
- None of these
- 300
- 250
- 350

**Q.**

If $p:Theearthisround,q:3+4=7$ then $\left(~p\right)\vee \left(~q\right)$ is

It is not that the earth is round or

The earth is round and

It is not that the earth is round or it is not that

The earth is round or $3+4=7$

The earth is round or it is not that $3+4=7$

**Q.**Given 5 different green dyes, four different blue dyes and three different red dyes, how many combinations of dyes can be chosen taking at least one green and one blue dye?

**Q.**The HCF and LCM of 36 and 15 are 'p' and 'q'. Find 'pxq'.

**Q.**None of the digits are repeated?

- 216
- 240
- 360
- 120
- 412

**Q.**The integers P, Q, R and S shown on the number line above are all equally spaced. If R and S are equal to 712 and 713, respectively, what is the value of P?

- 7
^{10} - 7
^{11} - -7
^{13} - 7
^{9} - none of these

**Q.**Assuming that no two consecutive digits are same, the number of n is

- n!
- 9!
- 9n
- n9

**Q.**You are Pramod Sharma residing at 80, Saket Nagar, Jabalpur. Your younger brother lives in a hostel. Write a letter of advice to your brother to set a goal in life and try to achieve it.

**Q.**

On 23rd Apr, 2001 it was Monday. What was the day of the week on 23rd Apr, 2000?

Monday

Sunday

Wednesday

Thursday

Tuesday

**Q.**Pupils of 10th standard of a school had arranged a function at a total cost of Rs. 1, 000 which was to be shared equally among them. Since 10 of them failed to join the function each of them had to pay Rs. 5 more. Find the number of pupils in the class.

**Q.**4 7 11 18 29 ? 76 123

- 53
- None of these
- 59
- 38
- 46