Question

ILL MEDAL!!!!!!
Suppose you pick 4 cards randomly from a well-shuffled standard deck of 52 playing cards.

The probability that you draw the 2, 4, 6, and 8 of spades in that order

A. 1/6,497,400
B. 1/380,204,032
C. 1/311,875,200

Answer 1

btw no picture..

Answer 2

Essentially it is a multiplication problem....

you want 4 distinct cards out of a deck of 52

the first one is 1 out of 52
the second one is 1 out of 51
the third one is 1 out of 50
the fourth one is 1 out of 49

Answer 3

(1/52) (1/51) (1/50) (1/49) = 1 / 6497400

Answer 4

The basis of the short cut described by @retirEEd is as follows:
The probability of drawing the specified 4 cards in any order is given by:
\[\large P(4\ specified\ cards)=\frac{\left(\begin{matrix}4 \\ 4\end{matrix}\right)\left(\begin{matrix}48 \\ 0\end{matrix}\right)}{\left(\begin{matrix}52 \\ 4\end{matrix}\right)}=\frac{4!48!}{52!}\]
The number of permutations of the 4 specified cards is 4!. Therefore the probability of drawing the cards is the specified order is:
\[\large P(4\ cards\ specified\ order)=\frac{4!48!}{52!4!}=\frac{1}{52\times51\times50\times49}\]

Answer 5

*in the specified order