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- Question
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
- Correct Answer
- 1/5525
Explanationn(S) = 52C3 = 132600/6 = 22100
n(E) = 4C3 = 24/6 = 4
- 1. 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
- 2. 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
- 3. 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
- 4. The number of permutations of the letters of the word 'MESMERISE' is ?
Options- A. 9!/(2!)^{2}x3!
- B. 9! x 2! x 3!
- C. 0
- D. None Discuss
- 5. A group of 10 representatives is to be selected out of 12 seniors and 10 juniors. In how many different ways can the group be selected if it should have at least one senior ?
Options- A. ²²C?? + 1
- B. ²²C? + ¹?C?
- C. ²²C??
- D. ²²C?? - 1 Discuss
- 6. 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
- 7. 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 Discuss
- 8. 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
- 9. 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
- 10. 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
Permutation and Combination problems
Search Results
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: 9!/(2!)^{2}x3!
Explanation:
n items of which p are alike of one kind, q alike of the other, r alike of another kind and the remaining are distinct can be arranged in a row in n!/p!q!r! ways.
The letter pattern 'MESMERISE' consists of 10 letters of which there are 2M's, 3E's, 2S's and 1I and 1R.
Number of arrangements =
Correct Answer: ²²C?? - 1
Explanation:
The total number of ways of forming the group of ten representatives is ²²C??.
The total number of ways of forming the group that consists of no seniors is ¹?C?? = 1 way
The required number of ways = ²²C?? - 1
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: 72
Explanation:
The 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
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.
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