Himstates website is aspired to provide you competitive exams information, questions and answers ,formulas etc. Permutation and Combination  is an important topic for competitive exams, entrance exams as well interviews.
So to benefit students formulas , questions and previous year questions on the topic of 'Permutation and Combination' is given below,
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• 'Permutation and Combination' important in which Competitive Exams ?
• Bank Competitive Exam
UPSC Competitive Exams
SSC Competitive Exams
Defense Competitive Exams
LIC or GIC  Exams
University Grants Commission or UGC
Common Aptitude Test or CAT
Career Aptitude Test
Railway Competitive Exam
MAT, GMAT, IBPS Exam, CSAT, CLAT

Permutation and Combination aptitude questions are also important in state(Himachal Pradesh) competitive exams of HPPSC, HPSSSB, HPBoSE and many more exams of Banking as well as entrance exams etc.

### Formulas For Topic 'Permutation and Combination'

Factorial Notation

Let n = positive integer. factorial n, denoted as n!
n! = n(n - 1)(n - 2)(n - 3) ... 3.2.1.
e. g.
6! = (6 x 5 x 4 x 3 x 2 x 1) = 720.
Permutations
The different arrangements of a given number of things by taking some or all at a time, are called permutations.
All permutations made with the letters x, y, z by taking two at a time are (xy, yx, xz, zx, yz, zy).
All permutations made with the letters x, y, z taking all at a time are:
( xyz, xzy, yxz, yzx, zxy, zyx).

### Questions On Topic 'Permutation and Combination '

Q. 1. Solve 30!/28!
A. 809
B. 870  (Ans)
C. 789
D. 678

Q. 2. Find maximum numbers of words that can be made from word "DAUGHTER" if  vowels always come together?
A. 4000
B. 4250
C. 4300
D. 4320  (Ans)

Q. 3. How many words can be made from letter "EXTRA" if vowels are never together?
A. 100
B. 110
C. 120  (Ans)
D. 90

Q. 4. In how many ways can a football 11 be chosen out of a batch of 15 players?
A. 1365  (Ans)
B. 1345
C. 1277
D. 1265

Q. 5. Find maximum numbers of words that can be made from word "DIRECTOR" so that all vowels come together?
A. 2190
B. 2156
C. 2160  (Ans)
D. None of these

Q. 6. In a team of 10 players, six are boys and 4 girls, four children are to be selected out of them.Find in how many different ways they can be selected so that at least one boy should is there?
A. 219
B. 209  (Ans)
C. 216
D. 200

Q. 7. Find how many three digits numbers can be made from given digits 7, 9, 5, 6, 2 & 3,
Condition :
1. Numbers must be divisible by 5
2. none of the digits is repeated?
A. 21
B. 29
C. 16
D. 20  (Ans)

Q. 8. Find in how many ways a group of five boys and two girls can be formed  out of total 7 boys and 3 girls.
A. 89
B. 63  (Ans)
C. 21
D. 126

Q. 9. In how many different ways can the letters made of a word "OPTICAL"?
Condition :
1. vowels always come together
A. 220
B. 4320
C. 720  (Ans)
D. None of these

Q. 10.In how many ways can the letters of the word "LEADER" be arranged?
A. 890
B. 630
C. 210
D. 360  (Ans)

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