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- Question
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
- Correct Answer
- 120960
ExplanationIn 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
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. 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
- 8. 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
- 9. How many ways are there to deal a five-card hand consisting of three eight's and two sevens?
Options- A. 36
- B. 72
- C. 24
- D. 16 Discuss
- 10. In how many ways can the letters of the word ABACUS be rearranged such that the vowels always appear together?
Options- A. 4!/2!
- B. 3!/2!
- C. (4! x 3!) / 2!
- D. 36 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 11760
Explanation:
Required number of ways= = ( )= 11760.
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: 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: 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
Correct Answer: 24
Explanation:
If a card hand that consists of four Queens and an Ace is rearranged, nothing has changed.
The hand still contains four Queens and an Ace. Thus, use the combination formula for problems with cards.
We have 4 eights and 4 sevens.
We want 3 eights and 2 sevens.
C(have 4 eights, want 3 eights) x C(have 4 sevens, want 2 sevens)
C(4,3) x C(4,2) = 24
Therefore there are 24 different ways in which to deal the desired hand.
Correct Answer: (4! x 3!) / 2!
Explanation:
ABACUS is a 6 letter word with 3 of the letters being vowels.
If the 3 vowels have to appear together, then there will 3 other consonants and a set of 3 vowels together.
These 4 elements can be rearranged in 4! Ways.
The 3 vowels can rearrange amongst themselves in 3!/2! ways as "a" appears twice.
Hence, the total number of rearrangements in which the vowels appear together are (4! x 3!)/2!
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