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- Question
From a total of six men and four ladies a committee of three is to be formed. If Mrs. X is not willing to join the committee in which Mr. Y is a member, whereas Mr.Y is willing to join the committee only if Mrs Z is included, how many such committee are possible?
Options- A. 91
- B. 104
- C. 109
- D. 98
- Correct Answer
- 91
ExplanationWe first count the number of committee in which
(i). Mr. Y is a member
(ii). the ones in which he is not
Case (i): As Mr. Y agrees to be in committee only where Mrs. Z is a member.
Now we are left with (6-1) men and (4-2) ladies (Mrs. X is not willing to join).
We can choose 1 more in5+ =7 ways.
Case (ii): If Mr. Y is not a member then we left with (6+4-1) people.
we can select 3 from 9 in =84 ways.
Thus, total number of ways is 7+84= 91 ways. - 1. A team of 8 students goes on an excursion, in two cars, of which one can seat 5 and the other only 4. In how many ways can they travel?
Options- A. 126
- B. 120
- C. 146
- D. 156 Discuss
- 2. How many arrangements can be made out of the letters of the word DRAUGHT, the vowels never beings separated?
Options- A. 1440
- B. 720
- C. 360
- D. 640 Discuss
- 3. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there?
Options- A. 209
- B. 290
- C. 200
- D. 208 Discuss
- 4. How many numbers of five digits can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits?
Options- A. 120
- B. 240
- C. 256
- D. 360 Discuss
- 5. 36 identical books must be arranged in rows with the same number of books in each row. Each row must contain at least three books and there must be at least three rows. A row is parallel to the front of the room. How many different arrangements are possible ?
Options- A. 5
- B. 6
- C. 7
- D. 8 Discuss
- 6. In how many different ways can the letters of the word 'HAPPYHOLI' be arranged?
Options- A. 89,972
- B. 90,720
- C. 72,000
- D. 81,000 Discuss
- 7. The letters of the word PROMISE are to be arranged so that three vowels should not come together. Find the number of ways of arrangements?
Options- A. 4320
- B. 4694
- C. 4957
- D. 4871 Discuss
- 8. In how many ways can letter of the word RAILINGS arrange so that R and S always come together?
Options- A. 1260
- B. 2520
- C. 5040
- D. 1080 Discuss
- 9. In a bag, there are 8 red, 7 blue and 6 green flowers. One of the flower is picked up randomly. What is the probability that it is neither red nor green ? A) 13 B)821 C)621 D)2021
Options- A. Option A
- B. Option B
- C. Option C
- D. Option D Discuss
- 10. In a group of 6 boys and 4 girls, four children are to be selected. In how many different ways can they be selected such that at least one boy should be there ?
Options- A. 205
- B. 194
- C. 209
- D. 159 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 126
Explanation:
There are 8 students and the maximum capacity of the cars together is 9.
We may divide the 8 students as follows
Case I: 5 students in the first car and 3 in the second
Case II: 4 students in the first car and 4 in the second
Hence, in Case I: 8 students are divided into groups of 5 and 3 in8C3 ways.
Similarly, in Case II: 8 students are divided into two groups of 4 and 4 in 8C4ways.
Therefore, the total number of ways in which 8 students can travel is:
=56 + 70= 126
Correct Answer: 1440
Explanation:
There are 7 letters in the word DRAUGHT, the two vowels are A and U. Since, the vowels are not to be separated, AU can be considered as one entity. Therefore, the number of letters will be 6 instead of 7. The permutations will be P(6,6) = 6! ways.
But the two vowels A and U can be arranged in two ways, i.e. AU and UA. The required number of arrangements = 2!.6! = 1440 ways.
Correct Answer: 209
Explanation:
We may have (1 boy and 3 girls) or (2 boys and 2 girls) or (3 boys and 1 girl) or (4 boys).
Required number of ways =
= = 209.
Correct Answer: 120
Explanation:
Required number of 5 digit numbers can be formed by using the digits 1, 0, 2, 3, 5, 6 which are between 50000 and 60000 without repeating the digits are
5 x 4 x 3 x 2 x 1 = 120.
Correct Answer: 5
Explanation:
The following arrangements satisfy all 3 conditions.
Arrangement 1: 3 books in a row; 12 rows.
Arrangement 2: 4 books in a row; 9 rows.
Arrangement 3: 6 books in a row; 6 rows.
Arrangement 4: 9 books in a row; 4 rows.
Arrangement 5: 12 books in a row; 3 rows.
Therefore, the possible arrangements are 5.
Correct Answer: 90,720
Explanation:
The given word HAPPYHOLI has 9 letters
These 9 letters can e arranged in 9! ways.
But here in the given word letters H & P are repeated twice each
Therefore, Number of ways these 9 letters can be arranged is
Correct Answer: 4320
Explanation:
Given Word is PROMISE.
Number of letters in the word PROMISE = 7
Number of ways 7 letters can be arranged = 7! ways
Number of Vowels in word PROMISE = 3 (O, I, E)
Number of ways the vowels can be arranged that 3 Vowels come together = 5! x 3! ways
Now, the number of ways of arrangements so that three vowels should not come together
= 7! - (5! x 3!) ways = 5040 - 720 = 4320.
Correct Answer: 5040
Explanation:
The number of ways in which the letters of the word RAILINGS can be arranged such that R & S always come together is
Count R & S as only 1 space or letter so that RS or SR can be arranged => 7! x 2!
But in the word RAILINGS, I repeated for 2 times => 7! x 2!/2! = 7! ways = 5040 ways.
Correct Answer: Option A
Explanation:
Total number of flowers = (8+7+6) = 21.
Let E = event that the flower drawn is neither red nor green.
= event taht the flower drawn is blue.
--> n(E)= 7
--> P(E)= =
Correct Answer: 209
Explanation:
We may have (1 boy and 3 girls)or(2boys and 2 girls)or(3 boys and 1 girl)or(4 boys).
Required number of ways = (
) +
+ (
) + (
)
= (24+90+80+15)
= 209.
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