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- Question
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?
Options- A. 15
- B. 10
- C. 25
- D. 20
- Correct Answer
- 25
ExplanationThe toys are different; The boxes are identical
If none of the boxes is to remain empty, then we can pack the toys in one of the following ways
a. 2,2,1
b. 3,1,1
Case a. Number of ways of achieving the first option 2?2?1
Two toys out of the 5 can be selected in 5 ways. Another 2 out of the remaining 3 can be selected in ways and the last toy can be selected in way.
However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2.
Therefore, total number of ways of achieving the 2?2?1 option is:
ways.
Case b. Number of ways of achieving the second option 3?1?1
Three toys out of the 5 can be selected in ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.
Therefore, total number of ways of getting the 3?1?1 option is =10 ways.
Total ways in which the 5 toys can be packed in 3 identical boxes
=number of ways of achieving Case a + number of ways of achieving Case b
=15 + 10 = 25 ways - 1. In how many ways can 4 sit at a round table for a group discussions?
Options- A. 9
- B. 3
- C. 6
- D. 12 Discuss
- 2. When Dr. Ram arrives in his dispensary, he finds 12 patients waiting to see him. If he can see only one patients at a time,find the number of ways, he can schedule his patients if 3 leave in disgust before Dr. Ram gets around to seeing them.
Options- A. 479001600
- B. 79833600
- C. 34879012
- D. 67800983 Discuss
- 3. In how many different ways can 3 students be associated with 4 chartered accountants,assuming that each chartered accountant can take at most one student?
Options- A. 12
- B. 36
- C. 24
- D. 16 Discuss
- 4. How many 3 letters words can be formed using the letters of the words hexagon?
Options- A. 120
- B. 210
- C. 160
- D. 200 Discuss
- 5. In how many ways can you choose one or more of 12 different candies?
Options- A. 4054
- B. 4050
- C. 4095
- D. 4059 Discuss
- 6. In how many different ways can 6 different balls be distributed to 4 different boxes, when each box can hold any number of ball?
Options- A. 2048
- B. 1296
- C. 4096
- D. 576 Discuss
- 7. What is the total no of ways of selecting atleast one item from each of the two sets containing 6 different items each?
Options- A. 2856
- B. 3969
- C. 480
- D. None of these Discuss
- 8. 16 persons are participated in a party. In how many differentways can they host the seat in a circular table, if the 2particular persons are to be seated on either side of the host?
Options- A. 16! × 2
- B. 14! × 2
- C. 18! × 2
- D. 14! Discuss
- 9. Two pipes A and B can fill a tank in 15 minutes and 20 minutes respectively. Both the pipes are opened together but after 4 minutes, pipe A is turned off. What is the total time required to fill the tank?
Options- A. 10 min. 20 sec.
- B. 11 min. 45 sec.
- C. 12 min. 30 sec.
- D. 14 min. 40 sec. Discuss
- 10. A pump can fill a tank with water in 2 hours. Because of a leak, it took 213 hours to fill the tank. The leak can drain all the water of the tank in:
Options- A. 7 hours
- B. 8 hours
- C. 12 hours
- D. 14 hours Discuss
Permutation and Combination problems
Search Results
Correct Answer: 6
Explanation:
We get this using the formula of circular permutations i.e., (4 - 1)! = 3! =6
Correct Answer: 79833600
Explanation:
There are 12 - 3 = 9 patients.They can be seen in = 79833600 ways
Correct Answer: 24
Explanation:
Number of permutations = = 24
Correct Answer: 210
Explanation:
Since the word hexagon contains 7 different letters,the number of permutations is = 7 x 6 x 5 =210
Correct Answer: 4095
Explanation:
Each candy can be dealt with in two ways.It can be chosen or not chosen.This will give 2 possibilites for the first candy, 2 for the second, and so on.by multiplying the cases together we get . Since the case of no candy being selected is not an option, we have to subtract 1 from our answer.
Therefore,there are - 1 = 4095 ways of selecting one or more candies
Correct Answer: 4096
Explanation:
Every ball can be distributed in 4 ways.
Hence the required number of ways = 4 x 4 x 4 x 4 x 4 x 4 = 4096
Correct Answer: 3969
Explanation:
We can select atleast one item from 6 different items =
Similarly we can select atleast one item from other set of 6 different items in ways.
Required number of ways = = 3969
Correct Answer: 14! × 2
Explanation:
(16 ? 2)! × 2 = 14! × 2
Correct Answer: 14 min. 40 sec.
Explanation:
Part filled in 4 minutes =4(1/15+1/20) = 7/15
Remaining part =(1-7/15) = 8/15
Part filled by B in 1 minute =1/20 : 8/15 :: 1:x
x = (8/15*1*20) =
The tank will be full in (4 min. + 10 min. + 40 sec.) = 14 min. 40 sec
Correct Answer: 14 hours
Explanation:
If the total area of pump=1 part
The pumop take 2 hrs to fill 1 part
The pumop take1 hour to fill 1/2 portion
Due to lickage
The pumop take 7/3 hrs to fill 1 part
The pumop take1 hour to fill 3/7 portion
Now the difference of area = (1/2-3/7)=1/14
This 1/14 part of water drains in 1 hour
Total area=1 part of water drains in (1x14/1)hours= 14 hours
So the leak can drain all the water of the tank in 14 hours.
Leak will empty the tank in 14 hrs
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