Latest IBM Aptitude Question SOLUTION: There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period? Option 1) 3200 2) 3600 3)

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There are 6 periods in each working day of a school. In how many ways can one organize 5 subjects such that each subject is allowed at least one period?

Option
1) 3200
2) 3600
3) 2400
4) None of these

Asked In IBM sanjana (9 years ago)

Unsolved Read Solution (7)

Is this Puzzle helpful?   (13)   (6) Submit Your Solution Permutation and Combination

Read Solution (7) :

uthra murugesan  (8 years ago)

5 subjects can be arranged in 6 periods in 6P5 ways.
Remaining 1 period can be arranged in 5P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (6P5 x 5P1)/2! = 1800

Alternatively this can be derived using the following approach.
5 subjects can be selected in 5C5 ways.
Remaining 1 subject can be selected in 5C1 ways.
These 6 subjects can be arranged themselves in 6! ways.
Since two subjects are same, we need to divide by 2!
Total number of arrangements = (5C5 × 5C1 × 6!)/2! = 1800

Is this solution Helpfull? Yes (25) | No (2)  

Harika Chowdary  (8 years ago)

ans: 3600
we have to arrange 5 subjects in 6 periods so 6P5=720
And we have one more period to assign the class. That means we have 5 possibilities to arrange the remaining period so total possibilities are
6P5 * 5=720*5=3600

Is this solution Helpfull? Yes (18) | No (13)  

uthra murugesan  (8 years ago)

5 subjects can be arranged in 6 periods in 6P5 ways.
Remaining 1 period can be arranged in 5P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid overcounting.
Total number of arrangements = (6P5 x 5P1)/2! = 1800

Alternatively this can be derived using the following approach.
5 subjects can be selected in 5C5 ways.
Remaining 1 subject can be selected in 5C1 ways.
These 6 subjects can be arranged themselves in 6! ways.
Since two subjects are same, we need to divide by 2!
Total number of arrangements = (5C5 × 5C1 × 6!)/2! = 1800

Is this solution Helpfull? Yes (3) | No (1)  

kritika gupta  (9 years ago)

here 6 period and 5 subjects present so
5 period 5 sub we assign as 5| and 6th period in 5 different ways so
5*(5!)=600

Is this solution Helpfull? Yes (2) | No (15)  

Amutha Jyothi  (7 years ago)

http://www.careerbless.com/aptitude/qa/discuss/permutations_combinations/discussion00000024322.php

correct ans 1800

Is this solution Helpfull? Yes (1) | No   

Rahul KUmar  (7 years ago)

5 subjects can be arranged in 6 periods in 6P5 ways.
Remaining 1 period can be arranged in 5P1 ways.
Two subjects are alike in each of the arrangement. So we need to divide by 2! to avoid double count.
Total number of arrangements = (6P5 x 5P1)/2! = 1800

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

manda chiranjeevi  (8 years ago)

there are total 5 places and in each place we can arrange in 6! ways

Is this solution Helpfull? Yes | No (4)  

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