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06 Aug 2006, 03:47
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Folks i think if someone can highlight the difference between those two problems , will make concepts more clear .. at least for me.
I have a major problem understanding the counting principles .
1st one:
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
20
30
50
600
Correct Answer is 50
2nd:
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
(1) 5C3
(2) 5P3
(3) 53
(4) 35
Correct Answer - (4)
I have a major problem understanding the counting principles .
1st one:
In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys?
20
30
50
600
Correct Answer is 50
2nd:
In how many ways can 5 letters be posted in 3 post boxes, if any number of letters can be posted in all of the three post boxes?
(1) 5C3
(2) 5P3
(3) 53
(4) 35
Correct Answer - (4)
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26 Dec 2006, 22:03
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The difference is simple; in the first question there can't be any empty boxes, whilst in the second there can be.
BTW, the answer for the second question is 3^5 and not 35
BTW, the answer for the second question is 3^5 and not 35
27 Dec 2006, 03:52
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yezz
5 different toys and 3 identical boxes
none of the boxes is to be empty, so there are two possibilities
(1) one box contains 3 toys and two boxes contain 1 toy each
Distribution - 3 :1:1
No. of ways = 5c3 * 2c1 * 1c1 = 20
(2) One box contains 1 toy and other two boxes contain 2 toys each
Distribution- 1:2:2
No. of ways= 5c1 * 4c2 * 2c2 = 30
Total no. of ways = 20+30 = 50
