GENiUSES!!Pls help me solve these complicated problems.Math geniuses.?

Question

I need help for these three questions but if can only sovle one two or three, i'll be very grateful.

1,. How many different 5-digit numbers can be formed using the digits 1; 2; 3; 4; and 5; without
repetition? (You don't have to list all these numbers.)

2,. If I have 3 different pairs of shoes, 2 dresses, and 2 jackets, how many different outfits are
possible to wear?

3,. We toss a coin twice in a row. List all possible outcomes. (For example, one possible outcome
is HT, i.e. head for the first, tail for the second toss.)
c

THANK YOU ALL FOR YOUR HELP.

Answer 1

1) 5! = 120 ways
5 choices for the first digit. Once that is chosen you have 4 choices for the 2nd digit, 3 choices for the 3rd, 2 choices for the 4th, 1 choice for the last.
5 x 4 x 3 x 2 x 1 = 120

2) 3 x 2 x 2 = 12 outfits, assuming you have to wear one of each.
3 choices for a pair of shoes. With that pair of shoes, you can wear one of two dresses, so you have 3 x 2 = 6 outfits so far. And with those you can pair one of two jackets. So that is 6 x 2 = 12. (Now if you are allowed to go without shoes, or without a jacket, or without a dress, that is a different question.)

3) 2 choices for the first toss, 2 choices for the second toss, so there should be a total of 4 outcomes:
HT
HH
TH
TT

Answer 2

1,. How many different 5-digit numbers can be formed using the digits 1; 2; 3; 4; and 5; without
repetition? (You don't have to list all these numbers.)

there are 5 numbers to choose from. & you will use them all. The answer is 5!=120

2,. If I have 3 different pairs of shoes, 2 dresses, and 2 jackets, how many different outfits are
possible to wear?

3*2*2=12

3,. We toss a coin twice in a row. List all possible outcomes. (For example, one possible outcome
is HT, i.e. head for the first, tail for the second toss.)

HH
HT
TH
TT

Answer 3

Not too complicated actually. Just think them through.
Question 1:
Start with the 5th place (ten thousands), we can place any of the 5 numbers there.
Moving to the 4th place (thousands), having placed one number, we can place any of 4 numbers here.
Working through this, the combinations are:
5x4x3x2x1 or 120
Question 2: Call the shoes A, B and C. Call the dresses M and N. Call the jackets R and S.
Consider shoes A. We can combine with dresses to get AM or AN. With either we can wear either jacket R or S, so we have the combinations AMR, AMS, ANR and ANS.
Repeat with for the other shoes, and we find 12 combinations.

3. If we are concerned with the order of outcomes, such as your HT, we have HH, HT, TH and TT.

Lots of luck

Answer 4

1. I'm assuming you mean the numbers cannot have 2 of the same digits? If so there are 5*4*3*2*1 possible combinations of a 5-digit number with these digits, or 120.

2. 3*2*2=12 (if they all match)

3. HH, HT, TH, TT

Answer 5

1,. How many different 5-digit numbers can be formed using the digits 1; 2; 3; 4; and 5; without
repetition? (You don't have to list all these numbers.)

At the start you intend to pull five digits from a five digit pool. So you can only get one 5-digit number from the pool of five digits.
After that the pool has zero left.
You are not looking for how many 1 digit numbers, plus how many 2 digit numbers .... how many 5 digit numbers I can get, from my understanding out of what you wrote. I take it you are only looking for how many five digit numbers can be pulled.

2. Answer = 12

3 Head & head, Head & tail, Tail & tail

Answer 6

1. This is called permutation, and the result is 5! = 120.
2. You can choose each separately,so there are 3 x 2 x 2 choices in all, or 12.
3. TT, TH, HT, HH. The middle two are probabilistically indistinguishable, but both count.

Answer 7

1) 5*4*3*2*1= 120
2) 3*2*2= 12
3) HT, TH, HH, TT

Answer 8

1. Number of combination = 5! = 120

2. Number of outfits = 3C1 x 2C1 x 2C1 = 12

3. HT, TH, HH, TT

Answer 9

1. 5*4*3*2*1
2. 3*2*2
3. hh ht tt th

Answer 10

1. Our old Earth. 2. A question. 3. Tommorow. 4. Fire.