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Bunuel
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How many five letter words (with or without meaning) can be formed suc 23 Mar 2020, 02:43
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95% (hard)

Question Stats:

38% (02:24) correct 62% (02:44) wrong based on 123 sessions

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How many five letter words (with or without meaning) can be formed such that the letters appearing in the odd positions are taken from the unrepeated letters of the word MATHEMATICS whereas the letters which occupy even places are taken from amongst the repeated letters of the same?


A. 3600
B. 540
C. 480
D. 420
E. 360


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How many five letter words (with or without meaning) can be formed suc Updated on: 23 Mar 2020, 03:29
Originally posted by lacktutor on 23 Mar 2020, 02:56.
Last edited by lacktutor on 23 Mar 2020, 03:29, edited 1 time in total.
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MATHEMATICS
—> Repeated: MAT (3 letters)
—> Unrepeated: HEICS (5 letters)

———1st —2nd—3rd—4th—5th
Odd —5 —————4————3—
Even ———3—————3————

—> 5*3*4*3*3 = 540 five-letter words

Answer (B)

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How many five letter words (with or without meaning) can be formed suc 23 Mar 2020, 03:15
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Unrepeated - 5 letters (H,E,I,C and S)
Repeated- 3 Letters (M, A and T)

There are 3 odd positions that are filled from 5 letters that are unrepeated in MATHEMATICS.
Total number of ways = 5C3 * 3! = 60

There are 2 even positions that are filled from 3 letters that are repeated in MATHEMATICS.

Total number of ways= 3C2*2! + 3C1*1 = 9

five letter words (with or without meaning) can be formed = 60*9= 540
Bunuel
How many five letter words (with or without meaning) can be formed such that the letters appearing in the odd positions are taken from the unrepeated letters of the word MATHEMATICS whereas the letters which occupy even places are taken from amongst the repeated letters of the same?


A. 3600
B. 540
C. 480
D. 420
E. 360

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How many five letter words (with or without meaning) can be formed suc 23 Mar 2020, 03:27
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Bunuel
How many five letter words (with or without meaning) can be formed such that the letters appearing in the odd positions are taken from the unrepeated letters of the word MATHEMATICS whereas the letters which occupy even places are taken from amongst the repeated letters of the same?


A. 3600
B. 540
C. 480
D. 420
E. 360
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MATHEMATICS
Repeated set of letters = 6 {M, A, T, M, A, T}.
Unrepeated set of letters = 5 {H, E, I, C, S}.

letters appearing in the odd positions are taken from the unrepeated letters
--> Number of possible ways of selecting = \(5c_3 = 10\)

letters which occupy even places are taken from amongst the repeated letters of the same = 2 letters
--> Number of 2 letters possible = {(M, M), (A, A), (T, T), (M, A), (A, T), (T, M)} = \(6\)

Case 1: When even places are of same digits.
Number of possible arrangements = \(5c_3*3!*3*1\) = \(180\) [\(5c_3*3!\) = Odd places; \(3*1\) = Even places]

Case 2: When even places are of different digits.
Number of possible arrangements = \(5c_3*3!*3*2! = 360\) [\(5c_3*3!\) = Odd places; \(3*2!\) = Even places]

--> Total number of arrangements possible = \(180 + 360 = 540\)

Option B
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How many five letter words (with or without meaning) can be formed suc 02 Nov 2023, 22:36
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