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- Question
A committee of 4 people is to be formed from a group of 9 people.How many possible committees can be formed?
Options- A. 120
- B. 162
- C. 126
- D. 170
- Correct Answer
- 126
ExplanationThis question is a combination since order is not important.
Answer = = 126
- 1. Goldenrod and No Hope are in a horse race with 6 contestants. How many different arrangements of finishes are there if No Hope always finishes before Goldenrod and if all of the horses finish the race?
Options- A. 720
- B. 360
- C. 120
- D. 640 Discuss
- 2. In how many ways, can zero or more letters be selected form the letters AAAAA?
Options- A. 5
- B. 6
- C. 2
- D. 8 Discuss
- 3. In how many ways can the letters of the word 'MISSISIPPI' be arranged ?
Options- A. 12400
- B. 11160
- C. 16200
- D. 12600 Discuss
- 4. There are 2 brothers among a group of 20 persons. In how many ways can the group be arranged around a circle so that there is exactly one person between the two brothers?
Options- A. 18! x 19!
- B. 2 x 19!
- C. 2 x 18!
- D. 18! x 18! Discuss
- 5. Eight first class and six second class petty officers are on the board of the 56 club. In how many ways can the members elect, from the board, a president, a vice-president, a secretary, and a treasurer if the president and secretary must be first class petty officers and the vice-president and treasurer must be second class petty officers?
Options- A. 1500
- B. 1860
- C. 1680
- D. 1640 Discuss
- 6. A pizza can have 3 toppings out of possible 7 toppings.How many different pizza's can be made?
Options- A. 49
- B. 35
- C. 27
- D. 25 Discuss
- 7. How many ways can you select 17 songs for mix CD out of possible 38 songs?
Options- A. 2878
- B. 2878 x 10^2
- C. 290183753
- D. 2878 x 10^10 Discuss
- 8. A school committee of 5 is to be formed from 12 students.How many committees can be formed if John must be on the committee?
Options- A. 11P4
- B. 11C4
- C. 11P5
- D. 11C5 Discuss
- 9. From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are there if the hand must contain 2 spades and 3 diamonds ?
Options- A. 7250100
- B. 7690030
- C. 7250000
- D. 3454290 Discuss
- 10. From a deck of 52 cards, a 5 card hand is dealt.How may distinct five card hands are there if the queen of spades and the four of diamonds must be in the hand?
Options- A. 52C5
- B. 50C3
- C. 52C4
- D. 50C4 Discuss
Permutation and Combination problems
Search Results
Correct Answer: 360
Explanation:
Two horses A and B, in a race of 6 horses... A has to finish before B
if A finishes 1... B could be in any of other 5 positions in 5 ways and other horses finish in 4! Ways, so total ways 5*4!
if A finishes 2... B could be in any of the last 4 positions in 4 ways. But the other positions could be filled in 4! ways, so the total ways 4*4!
if A finishes 3rd... B could be in any of last 3 positions in 3 ways, but the other positions could be filled in 4! ways, so total ways 3*4!
if A finishes 4th... B could be in any of last 2 positions in 2 ways, but the other positions could be filled in 4! ways, so total ways... 2 * 4!
if A finishes 5th .. B has to be 6th and the top 4 positions could be filled in 4! ways..
A cannot finish 6th, since he has to be ahead of B
Therefore total number of ways = 5*4! + 4*4! + 3*4! + 2*4! + 4! = 120 + 96 + 72 + 48 + 24 = 360
Correct Answer: 6
Explanation:
Selecting zero'A's= 1
Selecting one 'A's = 1
Selecting two 'A's = 1
Selecting three 'A's = 1
Selecting four 'A's = 1
Selecting five 'A's = 1
=> Required number ofways =6
Correct Answer: 12600
Explanation:
Total number of alphabets = 10
so ways to arrange them = 10!
Then there will be duplicates because 1st S is no different than 2nd S.
we have 4 Is 3 S and 2 Ps
Hence number of arrangements = 10!/4! x 3! x 2! = 12600
Correct Answer: 2 x 18!
Explanation:
fix one person and the brothers B1 P B2 = 2 ways to do so.
other 17 people= 17!
Each person out of 18 can be fixed between the two=18, thus, 2 x 17! x 18=2 x 18!
Correct Answer: 1680
Explanation:
Since two of the eight first class petty officers are to fill two different offices, we write 56
Then, two of the six second class petty officers are to fill two different offices; thus, we write =30
The principle of choice holds in this case; therefore, the members have 56 x 30 = 1680 ways to select the required office holders
Correct Answer: 35
Explanation:
There are 7 toppings in total,and by selecting 3,we will make different types of pizza.
This question is a combination since having a different order of toppings will not make a different pizza.
So, =35
Correct Answer: 2878 x 10^10
Explanation:
since it is a combination = = 2878 x 10^10
Correct Answer: 11C4
Explanation:
If John must be on the committee,we have 11 students remaining,out of which we choose 4. So,
Correct Answer: 7250100
Explanation:
There are 13 spades,we must include 2: 13
There are 13 diamonds,we must include 3:
Since we can't have more than 2 spades and 3 diamonds,the remaining 2 cards must be pulled out from the 26 remaining clubs and hearts :
Therefore, = 7250100
Correct Answer: 50C3
Explanation:
If the queen of spades and the four of diamonds must be in hand,we have 50 cards remaining out of which we are choosing 3.
So, 50
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