Combination
Each of the different groups or selections which can be made by some or all of a number of given things without reference to the order of the
things in each group is called a combination.
Mathematically The number of combinations of n different things taken r at a time is
Properties of Combination
Important Results on Combination
Important Points to be Remembered
1. Function
(i) If a set A has m elements and set B has n elements, then
(a) number of functions from A to B is n^{m}
(b) number of oneone function from A to B is ^{n}P_{m}, m ≤ n.
(c) number of onto functions from A to B is n^{m} — ^{n}C_{1}(n — 1)^{m} + ^{n}C_{2}(n — 2)^{m}…..; m ≤ n.
(d) number of increasing (decreasing) functions from A to B is ^{n}C_{m}, m ≤ n.
(e) number of nonincreasing (nondecreasing) functions from A to B is ^{m + n – 1}C_{m} .
(f) number of bijective (oneone onto) functions from A to B is n !, if m = n.
(ii) Number of permutations of n different objects taken r at a time in which m particular objects are always
(a) excluded = ^{n – m}P_{r}
(b) included = ^{n – m}P_{r – m} x r!
2. Geometry
3. Prime Factors
Any natural number > 1, can be expressed as product of primes.
4. Integral Solutions
5. Sum of Digits
6. Arrangements
7. Dearrangements
If n distinct objects are arranged in a row, then the number of ways in which they can be rearranged so that no one of them occupies the place assigned to it is
8. Selection
209 videos443 docs143 tests

1. What is combination in mathematics? 
2. How do you calculate the number of combinations? 
3. What is the difference between a combination and a permutation? 
4. Can repetitions occur in a combination? 
5. How are combinations used in reallife scenarios? 
209 videos443 docs143 tests


Explore Courses for JEE exam
