Rank of the word STARPLUS in the dictionary of words formed by letters of the word STARPLUS taken al

M4maths Previous Puzzles

10 Oct 2012 rank

Rank of the word STARPLUS in the dictionary of words formed by letters of the word STARPLUS taken all at a time?

OPtion

1) 12453
2) 12978
3) 12999
4) 13298
5) 13458
6) 13736
7) 14231
8) 14389
9) 14976
10) none of these

Solution

On arranging the letters of the word STARPLUS in order we will get
A,L,P,R,S,S,T,U
total no. of words = 8*7*6*5*4*3*2*1/2*1 = 20160
denominator 2*1 is present for the repetition of S in the word.
Rank = [20160/8]*4+[2520*2/7]*5+[720/6]*0+[120/5]*2+[24/4]*1+[6/3]*0+[2/2]*1+1 = 13736

Correct Option: 6 Best Solution (7)

souvik mondal   12 years AGO

Starting from "A" can form the word =(7!/2!)ways
Starting from "L" can form the word =(7!/2!)ways
Starting from "P" can form the word =(7!/2!)ways
Starting from "R" can form the word =(7!/2!)ways
Starting from "SA" can form the word =6!ways
Starting from "SL" can form the word =6!ways
Starting from "SP" can form the word =6!ways
Starting from "SR" can form the word =6!ways
Starting from "SS" can form the word =6!ways
Starting from "STAL" can form the word =4!ways
Starting from "STAP" can form the word =4!ways
Starting from "STARL" can form the word =3!ways
Starting from "STARPLS" can form the word =1!ways
Starting from "STARPLUS" can form the word =1!ways
so rank=(7!/2)+(7!/2)+(7!/2)+(7!/2)+6!+6!+6!+6!+6!+4!+4!+1!+1!=13736

Like? Yes (16) | No (3)  

Sri Harsha   12 years AGO

No. of words starting with:-
A-> 7!/2
L-> 7!/2
P-> 7!/2
R-> 7!/2
SA-> 6!
SL-> 6!
SP-> 6!
SR-> 6!
SS-> 6!
STAL-> 4!
STAP-> 4!
STARL-> 3!
STARPLS-> 1!
STARPLUS is next 1
Adding all these, we get
Rank= 13736

Like? Yes (5) | No (2)  

balu   12 years AGO

write alphabetical order ALPRSSTU
A=7!/2!,L=7!/2!,P=7!/2!,R=7!/2!,SA=6!,SL=SA=6! and so on add that one we get 13736

Like? Yes (5) | No (2)  

Ankit   12 years AGO

STARPLUS
Alphabet of atarplus in oder are - ALPRSSTU
NOW WE CALCULATE RANK OF STARPLUS
- WORD START FROM A - 7!/2 = 2520
- WORD START FROM L - 7!/2 = 2520
- WORD START FROM p - 7!/2 = 2520
- WORD START FROM R - 7!/2 = 2520
- WORD START FROM SA - 6! = 720
- WORD START FROM SL - 6! = 720
- WORD START FROM SP - 6! = 720
- WORD START FROM SR - 6! = 720
- WORD START FROM SS - 6! = 720
- WORD START FROM STAL - 4! = 24
- WORD START FROM STAP - 4! = 24
- WORD START FROM STARL - 3! = 6
- WORD START FROM STARPLSU - 1! = 1
sO, RANKO OF STARPLUS IS
2520+2520+2520+2520+720+720+720+720+720+24+24+1
=13736

Like? Yes (5) | No (3)  

Tijo Jose   12 years AGO

4 * (7!/2!) + 5 * 6! + 2 * 4! + 1 * 3! + 2

Like? Yes (3) | No (2)  

Anubhav Kumar   12 years AGO

permutation will be...
2520^4 + 720^5 + 24^2 +6 + 2
that will be 13736

Like? Yes (3) | No (4)  

susmit   12 years AGO

(7!/2)*4+(6!*5)+(4!)+(4!)+3!+2

Like? Yes (3) | No (4)