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Wednesday, 28 November 2012

Problem Solving : Permutation and combination Problem 3: If the letter of the word SEQUESTERED are arranged in all possible ways and these words are written out as in a dictionary form, then what is the 50th rank of the word SEQUESTERED is ?

If the letter of the word SEQUESTERED are arranged in all possible ways and these words are written out as in a dictionary form, then what is the 50th rank of the word SEQUESTERED is ?

Solution:

So the word SEQUESTERED can be arranged in dictionary form of letters as D E E E E Q R S S T U

Hence the number of words begin with DEEEEQR = 4! / 2! =12

and 
the number of words begin with DEEEEQS = 4! =24
the number of words begin with DEEEEQT = 4! / 2! =12

12+24+12 =48

so next word U becomes last word

hence next words are 49 and 50 will  be

DEEEEQURSST is 49th word

and
DEEEEQURSTS is the 50th word

and the answer --> 
50th rank of the word SEQUESTERED is "DEEEEQURSTS "

Cisco CCNA 1

Quantitative Aptitude : Problem Solving Skills

Problem Solving : Permutation and combination Problem 2: If the letter of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary form, then what is the rank of the word VERMA is ?

If the letter of the word VERMA are arranged in all possible ways and these words are written out as in a dictionary form, then what is the rank of the word VERMA is ?

Solution:

so the word VERMA letters of V, E, R, M, A

In alphabetical order A, E, M, R, V


So the number of words begin with A = 4! (leave A and consider remaining letters E, M, R, V)
and the number of words begin with E= 4! (leave A and consider remaining letters A, M, R, V)
and the number of words begin with M = 4! (leave A and consider remaining letters E, A, R, V)
and the number of words begin with R = 4! (leave A and consider remaining letters E, M, A, V)
after the word begins with V so here after consider two or more words combinations

So the number of words begin with VA = 3! (leave v and A and consider remaining 3 letters E,M, R)
VE becomes next character after VA set so below are the dictionary arrangement goes

1) VEAMR

2) VEARM
3) VEMAR
4) VEMRA

5) VERAM

finally 6) VERMA

Hence the Rank = 4! + 4! + 4! + 4! + 3! + 6 = 96 + 6+ 6 =108th Rank


Rank of the word VERMA is 108.

Monday, 26 November 2012

Problem Solving : Permutation and combination Problem 1 : In how many ways can the letter of the word PROPORTION be arranged by taking 4 letters at a time?

In how many ways can the letter of the word PROPORTION be arranged by taking 4 letters at a time?

Solution:

P R O P O R T I O N

below I've wrote letters without repeated words and then how many times particular word repeated
P R O T I N
P R O 
       O

Here (P, P) 2 P, (R, R) 2 R, and (O,O,O) 3 O

from the question here we gonna select 4 words hence we have the following chance to select those 4 words

Chance 1:   3 O and remaining 1 are different (That means (O,O,O)--> 3 word and (P,R,T,I,N) ---> 1 word from the 5)

Chance 2:  two of same words and other two of the  same words (here (O,O,O), (T,T) and (P,P) out of 3 pairs we gonna select 2 pair of words )

Chance 3: Two of same words and other two are different words (here (O,O,O), (T,T) and (P,P) out of 3 pairs we gonna select 1 pair of word and other 2 word from (R, O, I, N, T) words consider P,P has been selected pair  )

Chance 4: All 4 are different ( here P, R,  O, T, I , N out of 6 we gonna select 4 words)

Hence


Chance 1:  3C3 * 5C1 * (4! /3!) = 20 [3! for repeated words O,O,O]
Chance 2:  3C2 * (4! / (2!*2!)) = 18 [2! * 2! for repeated words of T,T and P,P]
Chance 3: 3C1*5C2 * (4! / 2!) = 360 [2! for repeated word T,T or P,P]
Chance 4: 6C4 * 4! = 360 [as usual]

finally add all the chances = 20 + 18 + 360 + 360 = 758 ways is the answer