There are 12 face cards in a standard deck of 52 cards. How many ways can you arrange a standard deck of 52 cards such that the first card is a face card?
A.12P1
B.12C1
C.12P1 × 51P51
D.12C1 × 51P51
E.12C1 × 51C51

Please help will give medal

Question

There are 12 face cards in a standard deck of 52 cards. How many ways can you arrange a standard deck of 52 cards such that the first card is a face card?
A.12P1
B.12C1
C.12P1 × 51P51
D.12C1 × 51P51
E.12C1 × 51C51

Please help will give medal

amistre64 · Answer

what have you considered?

amistre64 · Answer

remove a face card ... how many ways can you arrange 51 cards?

amistre64 · Answer

[face] :  51*50*49*...*3*2*1 

and there are 12 face cards so there are 12 different sets that you can make

mathmate · Answer

Even though 12P1 = 12C1, they have different meanings.
To distinguish between 12P1 and 12C1, think of the problem where the first 2 cards are face cards.