From a deck of 52 cards, a 7 card hand is dealt.How many distinct hands are ther

CuriousTab

CuriousTab

Home Aptitude

Discussion

Home ‣ Aptitude ‣ Permutation and Combination Comments

Question
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

Correct Answer

7250100

Explanation

There are 13 spades,we must include 2: 13 $C_{2}$

There are 13 diamonds,we must include 3: $13 C_{3}$

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 : $26 C_{2}$

Therefore, $13 C_{2} * 13 C_{3} * 26 C_{2}$ = 7250100

Permutation and Combination problems

Search Results

1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. In how many ways can you choose one or more of 12 different candies?
Options
A. 4054
B. 4050
C. 4095
D. 4059

8. How many 3 letters words can be formed using the letters of the words hexagon?
Options
A. 120
B. 210
C. 160
D. 200

9. In how many different ways can 3 students be associated with 4 chartered accountants,assuming that each chartered accountant can take at most one student?
Options
A. 12
B. 36
C. 24
D. 16

10. When Dr. Ram arrives in his dispensary, he finds 12 patients waiting to see him. If he can see only one patients at a time,find the number of ways, he can schedule his patients if 3 leave in disgust before Dr. Ram gets around to seeing them.
Options
A. 479001600
B. 79833600
C. 34879012
D. 67800983

Comments

More in Aptitude: