Combination:Each of the groups or selections which can be made by taking some or all of a number of things without reference to the order of things in each group is called a combination.
The number of combinations of n different things taken r at a time is
nCr = n!/[ r! (n -r)!]
For example, choosing two fruits out of a basket containing 4 oranges and 5 bananas - three combinations are possible - two oranges, two bananas or one orange and one banana.
Permutation:Each of the arrangements which can be made by taking some or all of a number of things is called permutation.
For example, the letters of word CAT can be arranged in six different waysCAT, CTA, ACT, ATC, TAC, TCA
Sometimes, students may be confused whether combination or permutation is being talked about. Certain key words/phrases can be helpful in deciding.
P(n, r) = n. (n -1). (n -2) ... (n -r +1) = n! / (n -r)
Combinations: Selection, choose, make group, distribute, committee, geometric problems.
Permutations: Arrangements, standing in a line, seated around a table, problems on digits or letters of a word.
Excersice
1. Evaluate: 30 ! / 28 !. a. 850 b. 860 c. 870 d. 880 e. None
2. Evaluate 60P3 : a. 205320 b. 202020 c. 535353 d. Cnat find e. None
3. Evaluate 10C3 : a. 120 b. 12 c. 1.20 d. 12.2 e. None
4. How many words can be formed by using all the letters of the word “BIHAR”.
a. 120 b. 12 c. 122 d. 112 e. None
5. How many words can be made from the letters of the word “ EXTRA”, so that the wovels are never together?
a. 72 b. 27 c. 87 d. Cant find e. None
6. How many words can be made from the letters of the word “ DIRECTOR”, so that the wovels are always together?
a. 2160 b. 1602 c. 2266 d. Cnat find e. None
7. In how many ways can a cricket team of 11 can be choosen out of a batch of 15 players?
a. 1365 b. 1333 c. 1444 d. Cnat find e. None
8 In how many ways, a committee of 5 members can be selected from 6 men and 5 ladies of 3 men and 2 ladies.
a. 100 b.200 c. 300 d. 400 e. None
9. How many words with or without meaning can be formed by using all the letters of the word “ APPLE”, using one letter exactly one time?
a. 720 b. 120 c. 60 d. 180 e. None
10. In how many different ways can the letter of the word “ RUMOUR” can be arranged?
a. 180 b. 90 c. 30 d. 720 e. None
11. How many words can be made from the letters of the word “ SIGNATURE”, so that the wovels are always together?
a. 720 b. 1440 c. 2880 d. 3600 e. 17280
12. A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the box, if at least one black ball is to be included in the draw?
a. 32 b. 48 c. 64 d. Cant Find e. None
Answer: 1b, 2a, 3a, 4a, 5a, 6a, 7a, 8b, 9c, 10a, 11e, 12c
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