Latest Infosys Aptitude Question SOLUTION: 7 members have to be selected from 12 men and 3 women ,Such that no two women can come together . In how many ways we can select them ?

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7 members have to be selected from 12 men and 3 women ,Such that no two women can come together .
In how many ways we can select them ?

Asked In Infosys subashini (8 years ago)

Unsolved Read Solution (9)

Is this Puzzle helpful?   (55)   (30) Submit Your Solution Permutation and Combination

Read Solution (9) :

harsh shah  (8 years ago)

since no two women can come together,therfore women can be selected in 3c1 ways ...and men will be chosen in 12c6 so to complete the 7 group members...
=12c6*3c1
and only selection of men also possible = 12c7

so final ans : 12c6*3c1 + 12c7

Is this solution Helpfull? Yes (36) | No (1)  

navaneet kumar  (8 years ago)

since no two women can come together,therfore women can be selected in 3c1 ways ...and men will be chosen in 12c6 so to complete the 7 group members...
so the answer would be=12c6*3c1

Is this solution Helpfull? Yes (28) | No (9)  

Gurfateh bhinder  (8 years ago)

step1) selecting random 7 person = 15c7

Step2)finding those cases when 2 women are together i.e (WW)_ _ _ _ _
which is equal to
3c2*13c5 (selecting 2 random women that will be together * selecting any 5 random people from l left 13)

Step3) subtacting those cases when 2 women are together from 15c7 ....
so 15c7 - (3c2 *12c5)

Is this solution Helpfull? Yes (12) | No   

abhinav bahl  (8 years ago)

THE QUESTION HAS ASKED TO SELECT THE OUTCOME NOT ARRANGE SO ONLY 2 CASES 12C7(WHEN NO WOMEN SELECTED)+ 12C6*3C1(WHEN 1 WOMEN SELECTED)

Is this solution Helpfull? Yes (4) | No   

AMAN KUMAR  (8 years ago)

when 0 women selected between 7 member
total number of ways of selection=12c7-----(1)
when 1 women selected between 7 member
total number of ways of selection=12c6*3c1-----(2)
when 2 women selected between 7 member
total number of ways of selection=12c5*3c2-6------(3)
here 6 is total number of selection of two women together
when 3 women selected between 7 member
total number of ways of selection=12c4*3c3-5-6--------(4)
here 5 is total number of selection of 3 women together
so the total number of selection way=(1)+(2)+(3)+(4)

Is this solution Helpfull? Yes (2) | No (7)  

paras   (8 years ago)

since no 2 women are to be together so choose choose only one women among the three in total we require 7mem. so 6 rom men and 1 women

Is this solution Helpfull? Yes (1) | No   

Shekhar  (8 years ago)

here we have 4 cases.
case 1-when no any women is selected --->in this case total selection of 7 members= 12c 7 ....... (1)
case 2-when 1 woman selected ---> total selection=3 c 1 *12 c 6 ......... (2)
case 3- when 2 women selected ----> total selection = 3 c2 * 12 c 5 - 6 ......(3) here 6 is the no of ways of selecting 2 girls together
case 4- when 3 girls taken ...> total selection =3 c 3 * 12 c 4 - 5 -6 .....(4) here 5 is the no of ways of selecting 3 women together nd 6 is the no of ways of selecting 2 women together

FOR 3 GIRLS TOGETHER PLACE THE REMAINING 4 BOYS .NOW WE HAVE 5 SPACE TO FILL B/W BOYS.THESE 5 SPACE CAN BE FILLED BY PLACING 3 GIRLS TOGETHER 5 TIMES. simiarly for 2 women together first we place 5 men then we have 6 space left to fill which can be filled by placing 2 women together 6times

total selection = (1)+ (2)+ (3)+ (4)

Is this solution Helpfull? Yes | No (3)  

shubham pancholi  (6 years ago)

There are 12 men Nd 3 women in which we cannot select two women together so first of all we will select 6men and 1women and then 7men . I.e 12c6*12c1+12c7*12c0

Is this solution Helpfull? Yes | No (1)  

Suganth  (5 years ago)

(12M6 * 3W1 ) + (12M4 * 3W3) = 27422+1045=28067

Is this solution Helpfull? Yes | No (6)  

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