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

the answer would be d

Step-by-step explanation:

 The correct option is (D)

Step-by-step explanation:  Given that there are 12 face cards in a standard deck of 52 cards.

We are to find the number of ways in which we can arrange a standard deck of 52 cards such that the first card is a face card.

Now, since there are 12 face cards, and the first card may be any one of theses 12 cards, so the number of ways in which the first card of 52 cards can be arranged is given by

Also, there are 51 cards left after the first card is arranged.

Now, out of these 51 cards, we need to choose all the 51 cards one by one and this is a situation of permutation.

So, the number of ways in which these 51 cards can be arranged is

Therefore, the total number of ways in which we can arrange a standard deck of 52 cards such that the first card is a face card will be

Thus, (D) is the correct option.

< 4, -5>

step-by-step explanation:

starting from g. we move 4 right and then 5 down to get to h. that means the vector is < 4, -5>

b) 1/3 * 1/5

step-by-step explanation:

each smallest part is 1/15 since the written one is 1/5 and it's divided by 3 equal parts. (1/5 )/3 = 1/15 = 1/3 * 1/5