Permutations and Combinations -2

Basics : Permutation – arrangementCombination – selection

• Out of n different things, if some or all the things are selected at a time,then each of these selections is called a Combination

• Out of n different things, if r things are selected at a time, then thenumber of selections is given by =

• and = ି• + + + + …..

• The number of ways in which we can select is given by .

Permutation – arrangementCombination – selection

• Out of n different things, if some or all the things are selected at a time,and arranged, then each of these arrangement is called a Permutation.

• N different things are selected all at a time can be arranged in n factorialways.

• Out of n different things, if r things are selected at a time and arranged,then the number of arrangements are given by =

Basics :

1. In how many ways can u arrange the letters of the word“SUCCESS”, such that all vowels all together?

2. In how many ways can u arrange 4 boys and 4 girls around acircular table such that, no 2 girls sit together?

3. How many 3 digit numbers can be formed using the digits1,2,3,4,5?

4. How many 4 digit numbers can be formed using the digits0,1,2,3,4,5 which are divisible by 4 (repetition of digits isallowed)?

Permutation :

In how many ways can u arrange the letters of the word “SUCCESS”?

Ans :NOTE: The number of ways in which we can arrange n things such that p things are alike, q things are alike, r things alike is given by .In the given question, C – 2, S – 3, E – 1, U – 1=> = 420

1.

number of ways = 420

S UC ECS S

In how many ways can u arrange the letters of the word “SUCCESS”,such that all ‘S’ are together?

Ans :NOTE: The number of ways in which we can arrange n things such that p things are alike, q things are alike, r things alike is given by .In the given question, C – 2, S – 3, E – 1, U – 1 = 60

1a.

number of ways = 60

SSS UC EC

In how many ways can u arrange the letters of the word “SUCCESS”,such that all vowels are together?

Ans :NOTE: The number of ways in which we can arrange n things such that p things are alike, q things are alike, r things alike is given by .In the given question, C – 2, S – 3, E – 1, U – 1=> = 120

1b.

number of ways = 120

S UEC CS S

In how many ways can u arrange 4 boys and 4 girls around a circulartable such that all boys sit together?

2.

Number of ways are = 576

NOTE :N different things can be arranges around circular table in (N-1)! Ways

G1G2G3G4

4! 5-1) !

B1B2B3B4

In how many ways can u arrange 4 boys and 4 girls around a circulartable such that no two girls sit together?

2a.

Number of ways are = 144

NOTE :N different things can be arranges around circular table in (N-1)! Ways

3! 5-1) ! 3! ! = 144

How many 3 digit numbers can be formed using the digits 1,2,3,4,5?3.Ans : _ _ _

=> = 3!Number that are formed by 3 digit numbers are = 60

How many 4 digit numbers can be formed using the digits 0,1,2,3,4,5?3a.Ans : _ _ _ _

5 5 4 3 => 5 4 3Number that are formed by 4 digit numbers are = 300

How many 4 digit numbers can be formed using the digits 0,1,2,3,4,5which are divisible by 4(repetition of digits is allowed)?

4.Ans :

Condition: last 2 digits should be divisible by 4 or the numbershould end with 2 zeroes.

_ _ _ _00,04,12,20,24,32,40,44,52 5 6 9

=> 5 9 = 270

Number that are formed by 4 digit numbers are = 270

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Problems for practice are given in the description of the video.

Practice problemson Permutations & Combinations

1. In how many ways can u arrange the letters of the word ___ such that notwo vowels are together, all consonants together, all vowels together, no twoconsonants together?1. “APTITUDE”2. “TRIANGLE”

2. In how many ways can u arrange the letters of the word “SPREAD” suchthat ALL vowels are together?

3. How many 4 digit numbers can be formed using the digits 0,1,2,3,4,5 which aredivisible by 4(repetition of digits is not allowed)?

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