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- Question
From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be formed if there are atleast 2 queens?
Options- A. 103336
- B. 120000
- C. 108336
- D. 108333
- Correct Answer
- 108336
ExplanationThe total possible cases would be a 5 card hand with no restrictions : 5
The unwanted cases are:
no queens(out of 48 non-queens cards we get 5)
only 1 queen(out of 4 queens we get 1,and out of 48 non-queens we get 4)
Therefore,
- 1. There are fourteen juniors and twenty-three seniors in the Service Club. The club is to send four representatives to the State Conference. If the members of the club decide to send two juniors and two seniors, how many different groupings are possible ?
Options- A. 23024
- B. 24023
- C. 23023
- D. 25690 Discuss
- 2. In how many ways can the letters of the word "PROBLEM" be rearranged to make 7 letter words such that none of the letters repeat?
Options- A. 49
- B. 7!
- C. 7^7
- D. 7^3 Discuss
- 3. 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
- 4. 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
- 5. 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
- 6. A student council of 5 members is to be formed from a selection pool of 6 boys and 8 girls.How many councils can have Jason on the council?
Options- A. 715
- B. 725
- C. 419
- D. 341 Discuss
- 7. How many arrangements of the word TRIGONAL can be made if only two vowels and three consonants are used?
Options- A. 6300
- B. 3600
- C. 6400
- D. 7200 Discuss
- 8. A research team of 6 people is to be formed from 10 chemists,5 politicians, 8 economists and 15 biologists.How many teams have atleast 5 chemists?
Options- A. 7350
- B. 6400
- C. 6379
- D. 7266 Discuss
- 9. There are 7 men and 10 women on a committee selection pool.A committee consisting of President,Vice-President, and Treasurer is to be formed.How many ways can exactly two men be on the committe ?
Options- A. 1200
- B. 1240
- C. 1260
- D. 1620 Discuss
- 10. If each of the 8 teams in a league must play each other three times,how many games will be played?
Options- A. 72
- B. 84
- C. 36
- D. 79 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 23023
Explanation:
Choose 2 juniors and 2 seniors.
Correct Answer: 7!
Explanation:
There are seven positions to be filled.
The first position can be filled using any of the 7 letters contained in PROBLEM.
The second position can be filled by the remaining 6 letters as the letters should not repeat.
The third position can be filled by the remaining 5 letters only and so on.
Therefore, the total number of ways of rearranging the 7 letter word = 7*6*5*4*3*2*1 = 7! ways.
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!
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
Explanation:
Since order does not matter, use the combination formula
= 24/6 = 4
Correct Answer: 715
Explanation:
If Jason is on th ecouncil,this reduces the selction pool to only 13 people,out of which we still need to select 4.
So, = 715
Correct Answer: 3600
Explanation:
First we need to choose two vowels and then three consonants . Now that we have 5 letters required to make the word,arrange them in 5! ways.
So,
Correct Answer: 7266
Explanation:
Correct Answer: 1260
Explanation:
There are ways of selecting two men, and ways of selecting a woman.Since each position in the committee is different,arrange the three people in 3! ways.
So,
Correct Answer: 84
Explanation:
Since,each member of the league must meet every other member of the league.If they only played each other once,there would be games.Since,each pairing of teams will occur three times,the answer will be triple.
Therfore, =84
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