From a deck of 52 cards, a 5 card hand is dealt.How many distinct hands can be f

CuriousTab

CuriousTab

Home Aptitude

Discussion

Home ‣ Aptitude ‣ Permutation and Combination See What Others Are Saying!

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

Explanation

The total possible cases would be a 5 card hand with no restrictions : $52 C_{5}$ 5

The unwanted cases are:

no queens(out of 48 non-queens cards we get 5) $48 C_{5}$

only 1 queen(out of 4 queens we get 1,and out of 48 non-queens we get 4) $4 C_{1} * 48 C_{4}$

Therefore, $52 C_{5} - (48 C_{5} + 4 C_{1} * 48 C_{4}) = 108336$

More questions

1.
Shankara buys a watch for Rs. 1,950 in cash and sells it for Rs. 2,200 at a credit of 1 year. If the rate of interest is 10% per annum, he _____ :
Options
A. gains Rs. 55
B. gains Rs. 50
C. loses Rs. 30
D. gains Rs. 30

5.
Rajan sold an articles for ? 6000 at a loss of 25%. Find the cost price.?
Options
A. ? 7500
B. ? 7200
C. ? 8000
D. ? 8500

6.
In which of the following cases, A = B?
Options
A. A = {12, 14, 16}, B = {16, 18, 20}
B. A = ?, b = {}
C. A = {x: x ? W and x < 1}, B = ?
D. A = {x: x is a day of the week beginning with S}, B = {Sunday}

8.
If two parallel lines are intersected by a transversal, then the bisectors of the two pairs of interior angles enclose a:
Options
A. Trapezium
B. Rectangle
C. Square
D. circle

10.
The length of minute hand of a wall clock is 7 cms. The area swept by minute hand in 30 minutes is?
Options
A. 147 sq. cm
B. 210 sq. cm
C. 154 sq. cm
D. 77 sq. cm

Comments

More in Aptitude: