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Permutation & Combination

Permutation & Combination. Permutation. No. of ways of arranging 4 letters a,b,c and d. Permutation. No. of ways of arranging 4 letters a,b,c and d. a. Permutation & Combination. b. 4. 4 ways to put into first place. c. 4 P 1 = 4. d. d. a. Permutation & Combination. b. 4.

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Permutation & Combination

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  1. Permutation & Combination

  2. Permutation No. of ways of arranging 4 letters a,b,c and d

  3. Permutation No. of ways of arranging 4 letters a,b,c and d

  4. a Permutation & Combination b 4 4 ways to put into first place c 4P1= 4 d

  5. d a Permutation & Combination b 4 4 ways to put into first place c

  6. c d a Permutation & Combination b 4 3 letters can be combined with every one letter in the first place.

  7. b a c d 4 Permutation & Combination 3 letters can be combined with every one letter in the first place.

  8. d a a b c b b c c Permutation & Combination d d c d a 4 X 3 3 letters can be combined with every one letter in the first place. d a b a b c

  9. There are 4x3=12 ways to arrange 4 letters in 2 places. a d a c b ab ac ad bc bd ba cd ca cb da db dc b b c c Permutation & Combination d d c d a 4 X 3 d a b a b c

  10. 2 letters can be combined with every one letter in the 2nd place. d a c b d c c b d a d a b c Permutation & Combination 4 X 3 d a b a b c

  11. 2 letters can be combined with every one letter in the 2nd place. d b c d c c a b d b d a c a b c a d a b Permutation & Combination 4 X 3

  12. c b b b c d c d a a d c b d a d a a b c c d d b b c d a a c c abcabd acdacb adbadcbcdbcabdabdcbac cd ca cb da db dc Permutation & Combination 4 X 3 x 2 There are 4x3x2=12x2=24 ways to arrange 4 letters in 3 places. 4P3= 4x3x2

  13. c b b b c d c d a a d c b d a d a a b c c d d b b c d a a c c d a b b d a d b c c a b a abcabd acdacb adbadcbcdbcabdabdcbacbad cda cdb cab cadcbacbddabdacdbcdbadcadcb Permutation & Combination 4 X 3 x 2 There are 4x3x2=12x2=24 ways to arrange 4 letters in 3 places. 4P3= 4x3x2

  14. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c c a d a b c-d d-c d-b b b c d a a c c d a b b d a d b c c a b ad Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  15. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c c a d a b c-d d-c d-b b-d b-c c-b d-a a a c c d a b b d a d b c c a b ad Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  16. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c c a d a b c-d d-c d-b b-d b-c c-b d-a a-d a-c c-a c d a b b d a d b c c a b ad Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  17. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c c a d a b c-d d-c d-b b-d b-c c-b d-a a-d a-c c-a c-d d-c a-b b-a b-d d-b a d b c c a b ad Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  18. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c c a d a b c-d d-c d-b b-d b-c c-b d-a a-d a-c c-a c-d d-c a-b b-a b-d d-b a-d d-a b-c c-b c a b a Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  19. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c c a d a b c-d d-c d-b b-d b-c c-b d-a a-d a-c c-a c-d d-c a-b b-a b-d d-b a-d d-a b-c c-b c-a a-c b-a a-b Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  20. 1 letter can be combined with every one letter in the 3rd place. d b c b c d a d b d a c a b c b a a c d c-d d-c d-b b-d b-c c-b d-a a-d a-c c-a c-d d-c a-b b-a b-d d-b a-d d-a b-c c-b c-a a-c b-a a-b abcdabdc acdbacbd adbcadcbbcdabcadbdacbdcabacdbacd cdab cdba cabd cadbcbadcbdadabcdacbdbcadbacdcbadcab Permutation & Combination 4 X 3 x 2 4P3= 4x3x2

  21. d b b b c d a d a c b d a c c a d a b c c-d d-c d-b b-d b-c c-b d-a a-d a-c c-a c-d d-c a-b b-a b-d d-b a-d d-a b-c c-b c-a a-c b-a a-b abcdabdc acdbacbd adbcadcbbcdabcadbdacbdcabacdbacd cdab cdba cabd cadbcbadcbdadabcdacbdbcadbacdcbadcab Permutation & Combination 4 X 3 x 2 x 1 There are 4x3x2x1=12x2=24 ways to arrange 4 letters in 4 places. 4P4= 4x3x2x1

  22. ac ca ab ba bd db bc cb ad da cd dc Combination No. of ways of selecting 2 letters from 4 letters a,b,c and d 2! ways 2! ways 2! ways 2! ways 2! ways 2! ways

  23. abc acb bac bca cab cba abd adb bad bda dab dba adc acd dac dca cad cda dbc dcb bdc bcd cdb cbd Combination No. of ways of selecting 3 letters from 4 letters a,b,c and d 3! ways 3! ways 3! ways 3! ways

  24. abcd abdc acdb acbd adbc adcb bacd badc bcda bcad bdac bdca cbad cbda cadb cabd cdba cdab dbca dbac dcab dcba dabc dacb Combination No. of ways of selecting 4 letters from 4 letters a,b,c and d 4! ways

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