Discussion
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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. 3739 + 164 x 27 =?
Options- A. 105400
- B. 4000
- C. 8200
- D. 690 Discuss
- 2. A solution of sugar syrup has 15 % sugar. Another solution has 5 % sugar. How many liter of the second solution must be added to 20 liters of the first solution to make a solution of 10 % sugar?
Options- A. 10
- B. 5
- C. 15
- D. 20 Discuss
- 3. If x = 997, y = 998, z = 999, then the value of x2 + y 2 + z 2 ? xy ? yz ? zx will be
Options- A. 3
- B. 9
- C. 16
- D. 4 Discuss
- 4. 190, 166, 145, 128, 112, 100, 91
Options- A. 100
- B. 166
- C. 145
- D. 128
- E. 112 Discuss
- 5. In how many ways can the letter of the word ' civilization' be arranged?
Options- A. 12! / 4!
- B. 12! / 4! -1
- C. 13! / 5! - 1
- D. None of these Discuss
- 6. From 4 officers and 8 Jawans in how many ways can 6 be chosen to include at least one officer?
Options- A. 896
- B. 986
- C. 886
- D. 996 Discuss
- 7. The average age of a man and his son is 27 yr. The ratio of their ages is 8 : 1, respectively. What will be the son's age after 6 yr?
Options- A. 6 yr
- B. 14 yr
- C. 12 yr
- D. 8 yr Discuss
- 8. If nP r= 720 nC r than the value r is?
Options- A. 6
- B. 5
- C. 4
- D. 7 Discuss
- 9. The average daily wages of staff, consisting of supervisors and labourers, of a company is Rs. 50. The average wages of supervisors is Rs. 150 while that of labourers is Rs. 40 per day. If the number of supervisors is 15, find the number of labourers in the company.
Options- A. 150
- B. 175
- C. 180
- D. 200 Discuss
- 10. If a fraction is multiplied by itself and then divided by the reciprocal of the same fraction, the result is 18 26/ 27. find the fraction?
Options- A. 8/27
- B. 11/3
- C. 22/3
- D. 32/3 Discuss
More questions
Correct Answer: 8200
Explanation:
3739 + 164 x 27 = ?
? = 3739 + 4428 = 8167 ? 8200
Correct Answer: 20
Explanation:
Correct Answer: 3
Explanation:
Correct Answer: 128
Explanation:
190 - 24 = 166 166 - 21 = 145 145 - 18 = 127 [Here, 128 is placed instead of 127] 127 - 15 = 112 112 - 12 = 100 ... and so on.
Therefore, 128 is wrong.
Correct Answer: 12! / 4! -1
Explanation:
There are 12 letters in the world 'civilization' of which four are i's and other are different letters.
? Total number of permutations = 12!/4!
But one word is civilization itself.
? Required number of rearrangements = 12!/4! - 1
Correct Answer: 896
Explanation:
We may choose 1 officer and 5 jawans or 2 officers and 4 jawans ......... or 4 officers and 2 jawans.
So Required answer = [4C1 x 8C5] + [4C2 x 8C4] + [4C3 x 8C3] + [4C4 x 8C2]
= 224 + 420 + 224 + 28 = 896.
Correct Answer: 12 yr
Explanation:
Let ages of man and his son are 8k yr and k yr, respectively .
According to the question,
(8k + k)/2 = 27
? k = (27 x 2)/9 = 6
Hence, age of son after 6 yr = 6 + 6 = 12 yr
Correct Answer: 6
Explanation:
We know that, nPr = nCrr!
? nPr = 720nCr
? nCr.r! = 720nCr
? r! = 720
? r = 6
Correct Answer: 150
Explanation:
As per figure we can calculate the ration as below.
Number of supervisors / Number of labourers = (10 / 100) = 1/10
Total number of labourers = Total no. of supervisors × 10
= 15 × 10 = 150.
Correct Answer: 22/3
Explanation:
If the required fraction be N.
Then, (N x N) / (1/N) = 1826/27
? N3 = 512 / 27
? N = 8/3 = 22/3
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