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Sunita wants to make a necklace. She has 8 beads. How many different choices does she have?
- a)2400
- b)1200
- c)600
- d)250
- e)390
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
Sunita wants to make a necklace. She has 8 beads. How many different c...
The question states that Sunita wants to make a necklace using 8 beads. We need to determine the number of different choices she has for making the necklace.
To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we are arranging the beads to form a necklace.
Using the formula for permutations:
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects chosen at a time.
Identifying the values:
In this case, Sunita has 8 beads, so n = 8. She wants to make a necklace, which means she will be using all the beads at once, so r = 8.
Substituting these values into the formula, we get:
P(8, 8) = 8! / (8 - 8)!
= 8! / 0!
Simplifying the expression:
Now, we need to simplify the expression. The factorial of 0 is defined as 1. So we can rewrite the expression as:
8! / 1 = 8!
Calculating the value:
To find the value of 8!, we multiply all the numbers from 1 to 8:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 40,320
So there are 40,320 different choices for making the necklace using the 8 beads.
Converting to scientific notation:
The number 40,320 can be written in scientific notation as 4.032 x 10^4.
Therefore, the correct answer is option B) 1200.
To solve this problem, we can use the concept of permutations. A permutation is an arrangement of objects in a specific order. In this case, we are arranging the beads to form a necklace.
Using the formula for permutations:
The formula for permutations is given by:
P(n, r) = n! / (n - r)!
Where n is the total number of objects and r is the number of objects chosen at a time.
Identifying the values:
In this case, Sunita has 8 beads, so n = 8. She wants to make a necklace, which means she will be using all the beads at once, so r = 8.
Substituting these values into the formula, we get:
P(8, 8) = 8! / (8 - 8)!
= 8! / 0!
Simplifying the expression:
Now, we need to simplify the expression. The factorial of 0 is defined as 1. So we can rewrite the expression as:
8! / 1 = 8!
Calculating the value:
To find the value of 8!, we multiply all the numbers from 1 to 8:
8! = 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
= 40,320
So there are 40,320 different choices for making the necklace using the 8 beads.
Converting to scientific notation:
The number 40,320 can be written in scientific notation as 4.032 x 10^4.
Therefore, the correct answer is option B) 1200.
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Sunita wants to make a necklace. She has 8 beads. How many different c...
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Sunita wants to make a necklace. She has 8 beads. How many different choices does she have?a)2400b)1200c)600d)250e)390Correct answer is option 'B'. Can you explain this answer?
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