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COMBINATION Formula and its application - 1 Follow Upvote

Combination Each of the different selections made by taking some or all of a number of objects, irrespective of their arrangement is called combination. Any difference Illustration 1 : List the different combinations formed of three letters A, B, C taken two at a time. Illustration 2 : List the different word formed of three letters A, B, C taken two at a time

Any difference Illustration 1 List the different combinations formed of three letters A, B, C taken two at a time. en meow Illustration 2 : List the different word formed of three letters A, B, C taken two at a time. eam

Difference between Apermutation and Combination In a combination only selection is made whereas in a permutation not only a selection is made but also an arrangement in a definite order is considered. In a combination, the ordering of the selected objects is immaterial whereas in a permutation, the ordering is essential. for example, AB and BA are same as combination but different as permutations. Practically to find the permutations of n different items, taken r at a time, we first select r items from n items and then arrange them. So, usually permutation exceeds the number of combinations. Each combinations corresponds to many permutations. For example, the six permutation ABC, ACB, BCA, BAC, CAB and CBA correspond to the same combination ABC

Difference between Apermutation and Combination In a combination only selection is made whereas in a permutation not only a selection is made but also an arrangement in a definite order is considered. In a combination, the ordering of the selected objects is immaterial whereas in a permutation, the ordering is essential. for example, AB and BA are same as combination but different as permutations. Practically to find the permutations of n different items, taken r at a time, we first select r items from n items and then arrange them. So, usually permutation exceeds the number of combinations. Each combinations corresponds to many permutations. For example, the six permutation ABC, ACB, BCA, BAC, CAB and CBA correspond to the same combination ABC. Generally we use the word arrangements for permutation and word selection for combinations.

Notation The number of all combinations of n objects, taken r at a time is generally denoted by rn

Basic calculation tip cn 2

Basic calculation tip cn 111 2

Basic calculation ti 0 2 3

Basic calculation ti 0 2 21 2o 3 2 20 C

If the ratio 2nC3 : "C3 is equal to 11 : 1, find value of n .4 b. 5 . 6 d.7

If the ratio n+2C3 : n-2 P4 is equal to 57 : 16, find value of n a. 14 b. 19 C. 20 d. 21

If -mC2, find value of m (m-1) 2 b. 6 c. mt)m(m-1)m-2) d. m#)m(m-1) 8 8

If -mC2, find value of m (m-1) 2 b. 6 c. mt)m(m-1)m-2) d. m#)m(m-1) 8 8 rm Cmcm mcm ) 2.

If -mC2, find value of a. (m-1) c. mt)m(m-1)m-2) 2 6 d. m#)m(m-1) 8 8 C2 2 2. 2

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