Discussion
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- Question
In a box, there are 5 black pens, 3 white pens and 4 red pens. In how many ways can 2 black pens, 2 white pens and 2 red pens can be chosen?
Options- A. 180
- B. 220
- C. 240
- D. 160
- Correct Answer
- 180
ExplanationNumber of ways of choosing 2 black pens from 5 black pens in ways.
Number of ways of choosing 2 white pens from 3 white pens in ways.
Number of ways of choosing 2 red pens from 4 red pens in ways.
By the Counting Principle, 2 black pens, 2 white pens, and 2 red pens can be chosen in 10 x 3 x 6 =180 ways.
- 1. The number of ways that 7 teachers and 6 students can sit around a table so that no two students are together is
Options- A. 7! x 7!
- B. 7! x 6!
- C. 6! x 6!
- D. 7! x 5! Discuss
- 2. To fill 8 vacancies there are 15 candidates of which 5 are from ST. If 3 of the vacancies are reserved for ST candidates while the rest are open to all, Find the number of ways in which the selection can be done ?
Options- A. 7920
- B. 74841
- C. 14874
- D. 10213 Discuss
- 3. Nine different letters of alphabet are given, words with 5 letters are formed from these given letters. Then, how many such words can be formed which have at least one letter repeated ?
Options- A. 43929
- B. 59049
- C. 15120
- D. 0 Discuss
- 4. In how many ways the letters of the word OLIVER be arranged so that the vowels in the word always occur in the dictionary order as we move from left to right ?
Options- A. 186
- B. 144
- C. 136
- D. 120 Discuss
- 5. There are three rooms in a Hotel: one single, one double and one for four persons. How many ways are there to house seven persons in these rooms ?
Options- A. 105
- B. 7! x 6!
- C. 7!/5!
- D. 420 Discuss
- 6. How many six digit odd numbers can be formed from the digits 0, 2, 3, 5, 6, 7, 8, and 9 (repetition not allowed)?
Options- A. 8640
- B. 720
- C. 3620
- D. 4512 Discuss
- 7. On the occasion of New Year, each student of a class sends greeting cards to the others. If there are 21 students in the class, what is the total number of greeting cards exchanged by the students?
Options- A. 380
- B. 420
- C. 441
- D. 400 Discuss
- 8. From a bunch of flowers having 16 red roses and 14 white roses, four flowers have to be selected. In how many different ways can they be selected such that at least one red rose is selected?
Options- A. 27405
- B. 26584
- C. 26585
- D. 27404 Discuss
- 9. A card is drawn from a pack of 52 cards. What is the probability that either card is black or a king?
Options- A. 15/52
- B. 17/26
- C. 13/17
- D. 15/26 Discuss
- 10. In how many different ways can the letters of the word 'RITUAL' be arranged?
Options- A. 720
- B. 5040
- C. 360
- D. 180 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 7! x 6!
Explanation:
The students should sit in between two teachers. There are 7 gaps in between teachers when they sit in a roundtable. This can be done in ways. 7 teachers can sit in (7-1)! ways.
Required no.of ways is =
Correct Answer: 7920
Explanation:
ST candidates vacancies can be filled by ways = 10
Remaining vacancies are 5 that are to be filled by 12
=> = (12x11x10x9x8)/(5x4x3x2x1) = 792
Total number of filling the vacancies = 10 x 792 = 7920
Correct Answer: 43929
Explanation:
Number of words with 5 letters from given 9 alphabets formed =
Number of words with 5 letters from given 9 alphabets formed such that no letter is repeated is =
Number of words can be formed which have at least one letter repeated =
= 59049 - 15120
= 43929
Correct Answer: 120
Explanation:
In given word OLIVER there are 3 vowels E, I & O. These can be arranged in only one way as dictionary order E, I & O.
There are 6 letters in thegiven word.
First arrange 3 vowels.
This can be done in 6C3 ways and that too in only one way.(dictionary order E, I & O)
Remaining 3 letters can be placed in 3 places = 3! ways
Total number of possible ways of arranging letters of OLIVER = 3! x ways = 6x5x4 = 120 ways.
Correct Answer: 105
Explanation:
Choose 1 person for the single room & from the remaining choose 2 for the double room & from the remaining choose 4 people for the four person room,
Then, 7C1 x 6C2 x 4C4
= 7 x 15 x 1 = 105
Correct Answer: 8640
Correct Answer: 420
Explanation:
Given total number of students in the class = 21
So each student will have 20 greeting cards to be send or receive (21 - 1(himself))
Therefore, the total number of greeting cards exchanged by the students = 20 x 21 = 420.
Correct Answer: 27404
Explanation:
Given total 16 Red roses and 14 White roses = 30 roses
Four flowers have to be selected from 30 i.e, = 27405 Ways
Now, atleast one Red rose is selected i.e, 27405(total) - 1(all four are white roses) = 27404 ways.
Correct Answer: 15/26
Explanation:
Number of cards in a pack of cards = 52
Number of black cards = 26
Number of king cards = 4 (2 Red, 2 Black)
Required, the probability that if a card is drawn either card is black or a king =
Correct Answer: 720
Explanation:
The number of letters in the given word RITUAL = 6
Then,
Required number of different ways can the letters of the word 'RITUAL' be arranged = 6!
=> 6 x 5 x 4 x 3 x 2 x 1 = 720
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