Math / Discrete

QuestionHow many four-letter sequences are possible that use the letters $b, p, h, w$ once each? $\square$ sequences

Studdy Solution

STEP 1

1. We are dealing with permutations of the letters $b, p, h, w$ .
2. Each letter is used exactly once in each sequence.
3. The order of the letters in the sequence matters.

STEP 2

1. Determine the number of letters to be arranged.
2. Use the formula for permutations.
3. Calculate the number of permutations.

STEP 3

Determine the number of letters to be arranged. We have four letters: $b, p, h, w$ .

STEP 4

Use the formula for permutations. The number of permutations of $n$ distinct objects is given by $n!$ .
$n = 4$
$\text{Permutations} = n! = 4!$

STEP 5

Calculate the factorial:
$4! = 4 \times 3 \times 2 \times 1 = 24$
The number of four-letter sequences possible is:
$\boxed{24}$

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QuestionHow many four-letter sequences are possible that use the letters $b, p, h, w$ once each? $\square$ sequences

Studdy Solution

STEP 1

1. We are dealing with permutations of the letters $b, p, h, w$ .
2. Each letter is used exactly once in each sequence.
3. The order of the letters in the sequence matters.

STEP 2

1. Determine the number of letters to be arranged.
2. Use the formula for permutations.
3. Calculate the number of permutations.

STEP 3

Determine the number of letters to be arranged. We have four letters: $b, p, h, w$ .

STEP 4

Use the formula for permutations. The number of permutations of $n$ distinct objects is given by $n!$ .
$n = 4$
$\text{Permutations} = n! = 4!$

STEP 5

Calculate the factorial:
$4! = 4 \times 3 \times 2 \times 1 = 24$
The number of four-letter sequences possible is:
$\boxed{24}$

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QuestionHow many four-letter sequences are possible that use the letters b,p,h,wb, p, h, wb,p,h,w once each? □\square□ sequences

Studdy Solution

STEP 1

1. We are dealing with permutations of the letters b,p,h,w b, p, h, w b,p,h,w.2. Each letter is used exactly once in each sequence.3. The order of the letters in the sequence matters.

STEP 2

1. Determine the number of letters to be arranged.2. Use the formula for permutations.3. Calculate the number of permutations.

STEP 3

Determine the number of letters to be arranged. We have four letters: b,p,h,w b, p, h, w b,p,h,w.

STEP 4

Use the formula for permutations. The number of permutations of n n n distinct objects is given by n! n! n!.n=4 n = 4 n=4Permutations=n!=4! \text{Permutations} = n! = 4! Permutations=n!=4!

STEP 5

Calculate the factorial:4!=4×3×2×1=24 4! = 4 \times 3 \times 2 \times 1 = 24 4!=4×3×2×1=24 The number of four-letter sequences possible is:24 \boxed{24} 24​

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Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

QuestionHow many four-letter sequences are possible that use the letters $b, p, h, w$ once each? $\square$ sequences

1. We are dealing with permutations of the letters $b, p, h, w$ .
2. Each letter is used exactly once in each sequence.
3. The order of the letters in the sequence matters.

1. Determine the number of letters to be arranged.
2. Use the formula for permutations.
3. Calculate the number of permutations.

Determine the number of letters to be arranged. We have four letters: $b, p, h, w$ .

Use the formula for permutations. The number of permutations of $n$ distinct objects is given by $n!$ .
$n = 4$
$\text{Permutations} = n! = 4!$

Calculate the factorial:
$4! = 4 \times 3 \times 2 \times 1 = 24$
The number of four-letter sequences possible is:
$\boxed{24}$