These Permutation and Combination questoins with solutions for CAT examination will help you to practice well for the actual CAT examination.

**1) Find the value of ‘n’ if 12 x n _{P6} =n_{P4}.**

a) 8

b) 11

c) 9

d) 7

**2) Find the value of x such that: 7 _{Cx}-1 + 7_{Cx} = 8_{Cx}+2**

a) 2

b) 3

c) 4

d) 5

**3) Find the maximum value of 16 _{Cx} for any natural number x.**

a) 6

b) 4

c) 7

d) 8

**4) If n _{Cr} = 5 and n_{Pr} = 120, then determine the value of n, r.**

a) 5, 3

b) 4, 2

c) 7, 4

d) 5, 4

**5) Determine the number of ways in which 5 prizes can be distributed among 4 students.**

a) 4^{5}

b) 5^{4}

c) 20

d) 5!/4

**6) How many different three-digit numbers can be formed with the digits 1, 2, 3, 4, 5 and 6.**

**So that none of the digits are repeated? **

a) 120

b) 130

c) 150

d) 100

**Directions for questions 7-8**

**7)How many 4 digit numbers greater than 5000 can be formed by using the digits 2, 3, 5, 6, 7 and 8 such that **

**None of the digits are repeated? **

a) 216

b) 240

c) 360

d) 120

**8) Digits can get repeated?**

a) 765

b) 432

c) 312

d) 864

**9) In how many ways can the letters of the word “CONVENIENCE” be arranged?**

a) 11!

b) 11!/[(2!)(3!) ]

c)11!/[(2!)(3!)(3!)]

d) 11!/3!

**10) In how many ways can the letters of the word “CONVENIENCE” be arranged so that they begin with 2Ns and end with 2Es?**

a) 7!

b) 11!/[(2!)(3!)(3!) ]

c)7!/3!

d) 7!/2!

**11) A triangle ABC has 2 points marked on the side BC, 5 points marked on the side CA and 3 points marked on side AB.**

None of these marked points is coincident with the vertices of the triangle ABC.

All possible triangles are constructed taking any three of thesepoints and the points A, B, C as the vertices.

**How many new triangles have atleast one vertex common with the triangle ABC? **

a) 256

b) 237

c) 207

d) 127

**12) If all the 5 letter words that can be formed using the letters of the word RASAM are arranged as in a dictionary, what will the rank of RASAM be?**

a) 40

b) 35

c) 41

d) 42

**13) Find the number of natural numbers which lie between 10 ^{8} and 10^{9} which have products of their digits as 6?**

a) 55

b)105

c)81

d) 92

**14) In a board meeting, 8 delegates from number 1 to 8 are sitting around a circular table.**

Number 4 and 5 always sit together and number 1 always sits next to number 4. If number 8 always sits exactly opposite number 3, how many can the seating be done?

a) 6!

b) 6_{C2} x 3

c) 4×3!

d) 4! x 2

**15) A bag has 3 red balls, 2 yellow balls and 3 black balls. They are drawn one by one and placed in a row.**

Find the number of ways they can be arranged.

a) 280

b) 410

c) 560

d) 712

**16) 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?**

a) 20

b) 22

c) 345

d) 465

**17) In a college a committee of 7 people has to be selected from a group of 8 fourth year and 6 third year students. In how many ways can this committee be selected if in the committee, majority of fourth year students is required?**

a) 2320

b) 1960

c) 1530

d) 2416

**Directions for questions 18-19**

**There are 5 boys and 4 girls. How many ways they can be arranged such that**

**18) No two girls are together**

a) 3600

b) 4200

c) 2400

d) none of these

**19) All girls are together**

a) 5!x4!

b) 6!x4!

c) 4!x3!

d) 9!

**20) How many different 7 digit numbers can be formed by using only 4,5,6 such that each of the numbers has the digit 4 appearing twice?**

a) 562

b) 672

c) 982

d) 1234

**21) A grid is set up as shown using 5 horizontal and 6 vertical lines. What are the number of ways one can go from point P to point Q walking along the grids but not moving upwards or left or retracing a grid?**

**22) 16 points are plotted on 3 parallel lines. What is the maximum number of triangles that can be drawn with these points?**

a) 416

b) 340

c) 520

d) none of these

**23) An eight digit number divisible by 9 is to be formed by using 8 digits out of the digits 0,1,2,3,4,5,6,7,8,9 without replacement.**

The number of ways in which can be done is

a) 9!

b) 2(7!)

c) 4(7!)

d) (36)(7!)

**24) How many 4-digit numbers that are divisible by 4 can be formed from the digits 1,2,3, 4 and 6?**

a) 36

b) 72

c) 24

d) None of these.

**25) There are 7 couples in a dance party. How many dance pairs can be there such that exactly 2 pairs are the original couples?**

a) 765

b) 924

c) 1222

d) 904

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