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- Question
A local delivery company has three packages to deliver to three different homes. if the packages are delivered at random to the three houses, how many ways are there for at least one house to get the wrong package?
Options- A. 3
- B. 5
- C. 3!
- D. 5!
- Correct Answer
- 5
ExplanationThe possible outcomes that satisfy the condition of "at least one house gets the wrong package" are:
One house gets the wrong package or two houses get the wrong package or three houses get the wrong package.
We can calculate each of these cases and then add them together, or approach this problem from a different angle.
The only case which is left out of the condition is the case where no wrong packages are delivered.
If we determine the total number of ways the three packages can be delivered and then subtract the one case from it, the remainder will be the three cases above.
There is only one way for no wrong packages delivered to occur. This is the same as everyone gets the right package.
The first person must get the correct package and the second person must get the correct package and the third person must get the correct package.
1×1×1=1
Determine the total number of ways the three packages can be delivered.
3×2×1=6
The number of ways at least one house gets the wrong package is:
6?1=5
Therefore there are 5 ways for at least one house to get the wrong package. - 1. When John arrives in New York,he has eight stops to see, but he has time only to visit six of them.In how many different ways can he arrange his schedule in New York?
Options- A. 20610
- B. 24000
- C. 20160
- D. 21000 Discuss
- 2. First,second and third prizes are to be awarded at an engineering fair in which 13 exhibits have been entered.In how many different ways can the prizes be awarded?
Options- A. 1736
- B. 1716
- C. 1216
- D. 1346 Discuss
- 3. In how many different ways can five persons stand in a line for a group photograph?
Options- A. 120
- B. 240
- C. 360
- D. 720 Discuss
- 4. If each of the 8 teams in a league must play each other three times,how many games will be played?
Options- A. 72
- B. 84
- C. 36
- D. 79 Discuss
- 5. There are 7 men and 10 women on a committee selection pool.A committee consisting of President,Vice-President, and Treasurer is to be formed.How many ways can exactly two men be on the committe ?
Options- A. 1200
- B. 1240
- C. 1260
- D. 1620 Discuss
- 6. A Group consists of 4 couples in which each of the 4 persons have one wife each. In how many ways could they be arranged in a straight line such that the men and women occupy alternate positions?
Options- A. 1152
- B. 1278
- C. 1296
- D. None of these Discuss
- 7. The Number of times the digit 8 will be written when listing the integers from 1 to 1000 is :
Options- A. 100
- B. 200
- C. 300
- D. 400 Discuss
- 8. There are 41 students in a class, number of girls is one more than number of guys. we need to form a team of four students. all four in the team cannot be from same gender. number of girls and guys in the team should NOT be equal. How many ways can such a team be made ?
Options- A. 49450
- B. 50540
- C. 46587
- D. 52487 Discuss
- 9. How many four digit even numbers can be formed using the digits {2, 7, 5, 3, 9, 1} ?
Options- A. 59
- B. 60
- C. 61
- D. 64 Discuss
- 10. If it is possible to make a meaningful word with the first, the seventh, the ninth and the tenth letters of the word RECREATIONAL, using each letter only once, which of the following will be the third letter of the word? If more than one such word can be formed, give ?X? as the answer. If no such word can be formed, give ?Z? as the answer.
Options- A. T
- B. X
- C. N
- D. R Discuss
Permutation and Combination problems
Search Results
Correct Answer: 20160
Explanation:
He can arrange his schedule in = 20160 ways
Correct Answer: 1716
Explanation:
= 13!/10! = 1716
Correct Answer: 120
Explanation:
This is the number of permutations of five things taken all at a time.
Therefore, answer = = 120 ways
Correct Answer: 84
Explanation:
Since,each member of the league must meet every other member of the league.If they only played each other once,there would be games.Since,each pairing of teams will occur three times,the answer will be triple.
Therfore, =84
Correct Answer: 1260
Explanation:
There are ways of selecting two men, and ways of selecting a woman.Since each position in the committee is different,arrange the three people in 3! ways.
So,
Correct Answer: 1152
Explanation:
Case I : MW MW MW MW
Case II: WM WM WM WM
Let us arrange 4 men in 4! ways, then we arrange 4 women in 4P4 ways at 4 places either left of the men or right of the men. Hence required number of arrangements
Correct Answer: 300
Explanation:
Since 8 does not occur in 1000, we have to count the number of times 8 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form xyz, where
Let us first count the numbers in which 8 occurs exactly once.
Since 8 can occur atone place in ways. There are such numbers.
Next, 8 can occur in exactly two places in such numbers. Lastly, 8 can occur in all three digits in one number only.
Hence, the number of times 8 occur is
Correct Answer: 50540
Explanation:
Given G + B= 41 and B = G-1
Hence, G = 21 and B = 20
Now we have 2 options,
1G and 3M
(or)
3G and 1M
(2G and 2M or 0G and 4M or 4G and oM are not allowed),
Total : = 50540 ways.
Correct Answer: 60
Explanation:
The given digits are 1, 2, 3, 5, 7, 9
Number of even numbers = ?P? = 60.
Correct Answer: R
Explanation:
The first, the seventh, the ninth and the tenth letters of the word RECREATIONAL are R, T, O and N respectively. Meaningful word from these letters is only TORN. The third letter of the word is ?R?.
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