Question

determine the no of card combination out of 52 cards if there is exactly 2kings in each combination

Answer 1

Step-by-step explanation:

The observation that in a deck of 52 cards we have 4 kings and 48 non kings.

Selection of 5 cards having at least one king can be made as follows:

1 king and 4 non kings or 2 kings and 3 non kings or 3 kings and 2 non kings or 4 kings and 1 non king.

This can be expressed mathematically as

Number of selections:

4

C

1

×

48

C

4

+

4

C

2

×

48

C

3

+

4

C

3

×

48

C

2

+

4

C

4

×

48

C

1

=

3!1!

4!

×

44!4!

48!

+

2!2!

4!

×

45!3!

48!

+

3!1!

4!

×

46!2!

48!

+

47!1!

48!

=4×

4×3×2

48×47×46×45

+

3×2

48×47×46

+4×

2

48×47

+48

=778320+103776+4512+48

=886656