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                        Permutation or Arrangement

Number of ways in which ‘n’ different onjects can be arranged:
Total object = n 
& n object will occupy n different places.

n (n-1) (n-2) (n-3) ........ 1n places

∴ total numbere of ways = n×(n-1)×(n-2)×(n-3)×…………×1
                                             = n!
Hence

'n' distinct objects can be arranged in n! ways

Example:- In how many ways 20 students can be arranged in a straight line?
Solution:-

20! Answer

Example:- In how many ways 20 similar objects can be arranged in a straight line?
Solution:-

Since objects are similar
∴ number of ways = 1 Answer

Example:- In how many ways 5 students can be arranged on 10 chairs in a straight line?
Solution:- 

Always remember : ” First select & then arrange”
∴ 
5 chair can be selected out of 10 chairs in ¹⁰C₅ ways.
now 5 students can be arranged in these 5 chairs in 5! ways
Hence total number of ways = ¹⁰C₅×5!
¹⁰P₅ Answer

Example:- There are 10 students in a class. If three particular students Suresh, Amit & Ankit are to always sit together then in how many ways these 10 students vcasnm be arranged in a straight line?
Solution:-

1234567(8910)SureshAmitAnkit8

= 8!.3! ways Answer

Example:-  In above question if three particular students never sit together.
Solution:-
(
10
! – 8!.3!) ways Answer
Example:-
In how many ways 20 students can be arranged in a straight line if four students A, B, C, D are always together & B is always at last of A, B, C.
Solution:-

(ACDB)3! ways1 way

= 20 – 4 + 1
= 17
Hence total number of ways = 17!.3!.1
                                                    = 17!.3! ways Answer

Example:- How many 5 digit numbers can be formed out of digits 1, 2, 3, 7, 9. if repetition of digit is not allowed.
Solution:- 

5 4 3 2 1

= 5×4×3×2×1
= 5! ways Answer