Question

Four points question: Answer the following A- When selecting cards from a deck without replacing, the number of ways to draw the 3 card is (which of the following)? 52 52-1 52-2 B- When calculating the number of permutations of all letters in a word, the denominator of the calculation is which of the following? n! 0! C- How many ways can you draw a card from a normal deck and roll a number on a normal die? D- If you pick cards from a normal deck of cards, one at a time and replace the card and reshuffle the deck between draws, how many ways can you select 3 cards?

Answer 1

Answer:

A : 52-2

B : 0!

C : 312

D : 140608

Step-by-step explanation:

Part A:

It is given that that cards are selecting from a deck without replacing. So,

The number of ways to draw first card = 52

Now, one card is draw. The remaining cards are 51.

The number of ways to drawn second card = 52 - 1 =51

Now, one more card is drawn. The remaining cards are 50.

The number of ways to drawn third card = 52 - 2 =50

Therefore the number of ways to draw the 3 card is 52-2.

Part B:

Let a word has n letters and we need to find the number of permutations of all letters in a word, then the permutation formula is

$^nP_n=\frac{n!}{(n-n)!}=\frac{n!}{0!}$

The denominator of the calculation is 0!.

Part C:

Total number of cards is a normal deck = 52

Total number sides in a die = 6

Total number of ways to draw a card from a normal deck and roll a number on a normal die = 52 × 6 = 312.

Therefore the total number of ways to draw a card from a normal deck and roll a number on a normal die is 312.

Part D:

It is given that we pick cards from a normal deck of cards, one at a time and replace the card and reshuffle the deck between draws.

Total number of ways to select each card = 52

Total number of ways to select 3 cards = 52³ = 140608

Therefore the total number of ways to select 3 cards is 140608.