Math  /  Discrete

QuestionUse the formula for npr\mathrm{n}^{p_{\mathrm{r}}} to solve.
A church has 10 bells in its bell tower. Before each church service 4 bells are rung in sequence. No bell is rung more than once. How many sequences are there? A) 151,200 B) 210 C) 5040 D) 302.400

Studdy Solution

STEP 1

What is this asking? How many different ways can we ring 4 bells out of a total of 10 bells, one after the other? Watch out! The order in which the bells are rung matters, so it's about sequences (permutations), not combinations!

STEP 2

1. Understand Permutations
2. Calculate the Number of Sequences

STEP 3

We have 10 bells to choose from for the first ring.
After ringing one bell, we only have 9 bells left for the second ring.
Then 8 bells for the third ring, and finally 7 bells for the fourth ring.
This is what we call a *permutation*, where the order matters!

STEP 4

Let's **calculate** the number of sequences.
For the first bell, we have 10\text{10} choices.

STEP 5

For the second bell, we have 9\text{9} choices left.

STEP 6

For the third bell, we have 8\text{8} choices remaining.

STEP 7

And for the fourth bell, we have 7\text{7} choices.

STEP 8

To get the **total number of sequences**, we **multiply** these numbers together: 1098710 \cdot 9 \cdot 8 \cdot 7.
Why multiply?
Because each choice of the first bell can be combined with each choice of the second bell, and so on!

STEP 9

Let's do the **multiplication**: 109=9010 \cdot 9 = 90 908=72090 \cdot 8 = 7207207=5040720 \cdot 7 = 5040

STEP 10

There are **5040** different sequences.
So the answer is C!

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