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- Question
Suppose you can travel from a place A to a place B by 3 buses, from place B to place C by 4 buses, from place C to place D by 2 buses and from place D to place E by 3 buses. In how many ways can you travel ?from A to E?
Options- A. 36
- B. 64
- C. 74
- D. 72
- Correct Answer
- 72
ExplanationThe bus fromA to B can be selected in 3 ways.
The bus from B to C can be selected in 4 ways.
The bus from C toD can be selected in 2 ways.
The bus fromD to E can be selected in 3 ways.
So, by the General Counting Principle, one can travel fromA to E in 3 x 4 x 2 x 3 ways = 72
- 1. In a G - 20 meeting there were total 20 people representing their own country. All the representative sat around a circular table. Find the number of ways in which we can arrange them around a circular table so that there is exactly one person between two representatives namely Manmohan and Musharraf.
Options- A. 2 x (17!)
- B. 2 x (18!)
- C. (3!) x (18!)
- D. (17!) Discuss
- 2. From a pack of 52 cards, 3 cards are drawn together atrandom, What is the probability of both the cards are king?
Options- A. 1/5225
- B. 1/5525
- C. 5525
- D. 1/525 Discuss
- 3. How many 4-digit numbers can be formed from the digits 2, 3, 5, 6, 7 and 9, which are divisible by 5 and none of the digits is repeated?
Options- A. 60
- B. 48
- C. 36
- D. 20 Discuss
- 4. In how many ways word of 'GLACIOUS' can be arranged such that 'C' always comes at end?
Options- A. 3360
- B. 5040
- C. 720
- D. 1080 Discuss
- 5. A group consists of 4 men, 6 women and 5 children. In how many ways can 2 men , 3 women and 1 child selected from the given group ?
Options- A. 600
- B. 610
- C. 609
- D. 599 Discuss
- 6. In how many ways a committee, consisting of 5 men and 6 women can be formed from 8 men and 10 women?
Options- A. 11670
- B. 12000
- C. 11760
- D. 20050 Discuss
- 7. In how many different ways can the letters of the word 'MATHEMATICS' be arranged so that the vowels always come together?
Options- A. 120960
- B. 120000
- C. 146700
- D. None of these Discuss
- 8. Find the total number of distinct vehicle numbers that can be formed using two letters followed by two numbers. Letters need to be distinct
Options- A. 65000
- B. 64000
- C. 72000
- D. 36000 Discuss
- 9. 12 points lie on a circle. How many cyclic quadrilaterals can be drawn by using these points?
Options- A. 500
- B. 490
- C. 495
- D. 540 Discuss
- 10. Find the number of ways to take 4 people and place them in groups of 3 at a time where order does not matter?
Options- A. 4
- B. 12
- C. 36
- D. 16 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 2 x (18!)
Explanation:
A person can be chosen out of 18 people in 18 ways to be seated between Musharraf and Manmohan. Now consider Musharraf, Manmohan, and the third person, sitting between them, as a single personality, we can arrange them in 17! ways but Musharraf and Manmohan can also be arranged in 2 ways.
Required number of permutations = 18 x (17!) x 2 = 2 x 18!
Correct Answer: 1/5525
Explanation:
n(S) = 52C3 = 132600/6 = 22100
n(E) = 4C3 = 24/6 = 4
Correct Answer: 60
Explanation:
Here given the required digit number is 4 digit.
It must be divisible by 5. Hence, the unit's digit in the required 4 digit number must be 0 or 5. But here only 5 is available.
x x x 5
The remaining places can be filled by remaining digits as 5 x 4 x 3 ways.
Hence, number 4-digit numbers can be formed are 5 x 4 x 3 = 20 x 3 = 60.
Correct Answer: 5040
Explanation:
Given word is GLACIOUS has 8 letters.
=> C is fixed in one of the 8 places
Then, the remaining 7 letters can be arranged in 7! ways = 5040.
Correct Answer: 600
Explanation:
Two men, three women and one child can be selected in ?C? x ?C? x ?C? ways = 600 ways.
Correct Answer: 11760
Explanation:
Required number of ways= = ( )= 11760.
Correct Answer: 120960
Explanation:
In the word 'MATHEMATICS', we treat the vowels AEAI as one letter.
Thus, we have MTHMTCS (AEAI).
Now, we have to arrange 8 letters, out of which M occurs twice, T occurs twice and the rest are different.
Number of ways of arranging these letters = 8!/(2! x 2!)= 10080.
Now, AEAI has 4 letters in which A occurs 2 times and the rest are different.
Number of ways of arranging these letters =4!/2!= 12.
Required number of words = (10080 x 12) = 120960
Correct Answer: 65000
Explanation:
Out of 26 alphabets two distinct letters can be chosen in ways. Coming to numbers part, there are 10 ways.(any number from 0 to 9 can be chosen) to choose the first digit and similarly another 10ways to choose the second digit. Hence there are totally 10X10 = 100 ways.
Combined with letters there are X 100 ways = 65000 ways to choose vehicle numbers.
Correct Answer: 495
Explanation:
For any set of 4 points we get a cyclic quadrilateral. Number of ways of choosing 4 points out of 12 points is = 495.
Therefore, we can draw 495 quadrilaterals
Correct Answer: 4
Explanation:
Since order does not matter, use the combination formula
= 24/6 = 4
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