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Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?
- a)956
- b)756
- c)9!
- d)7560
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pin...
1 balloon is fixed that is to be placed above the cake
Now she have to arrange 9 balloons = 9!/(5!*2!*2!)
(9*8*7*6*5!)/((5!*2*2)
= (9*8*7*6)/(2*2)
= 756
Now she have to arrange 9 balloons = 9!/(5!*2!*2!)
(9*8*7*6*5!)/((5!*2*2)
= (9*8*7*6)/(2*2)
= 756
Most Upvoted Answer
Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pin...
To solve this problem, we need to use the concept of permutations. Permutations are arrangements of objects in a specific order. In this case, we need to find the number of ways Sonia can arrange the 10 balloons.
Step 1: Calculate the total number of arrangements
The total number of arrangements of 10 balloons can be calculated using the formula for permutations of n objects taken r at a time, which is given by:
nPr = n! / (n-r)!
In this case, we have 10 balloons and we want to arrange all of them, so r = 10.
Therefore, the total number of arrangements is:
10P10 = 10! / (10-10)! = 10!
Step 2: Adjust for the balloons behind the cake table
Out of the 10 balloons, Sonia wants to place the pink balloon at the center of the room above the cake table, and the remaining 9 balloons at the wall behind the cake table. This means that the arrangement of the 9 balloons behind the cake table does not matter.
Step 3: Calculate the number of ways to arrange the remaining 9 balloons
The number of ways to arrange the remaining 9 balloons can be calculated using the formula for permutations, where we have 9 objects and we want to arrange all of them:
9P9 = 9! / (9-9)! = 9!
Step 4: Multiply the results from steps 2 and 3
To find the total number of ways to arrange the balloons, we multiply the results from steps 2 and 3:
Total number of ways = 10! * 9!
Simplifying this expression, we get:
Total number of ways = 10! * 9! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
This simplifies to:
Total number of ways = 9!
Therefore, the correct answer is option B) 756.
Step 1: Calculate the total number of arrangements
The total number of arrangements of 10 balloons can be calculated using the formula for permutations of n objects taken r at a time, which is given by:
nPr = n! / (n-r)!
In this case, we have 10 balloons and we want to arrange all of them, so r = 10.
Therefore, the total number of arrangements is:
10P10 = 10! / (10-10)! = 10!
Step 2: Adjust for the balloons behind the cake table
Out of the 10 balloons, Sonia wants to place the pink balloon at the center of the room above the cake table, and the remaining 9 balloons at the wall behind the cake table. This means that the arrangement of the 9 balloons behind the cake table does not matter.
Step 3: Calculate the number of ways to arrange the remaining 9 balloons
The number of ways to arrange the remaining 9 balloons can be calculated using the formula for permutations, where we have 9 objects and we want to arrange all of them:
9P9 = 9! / (9-9)! = 9!
Step 4: Multiply the results from steps 2 and 3
To find the total number of ways to arrange the balloons, we multiply the results from steps 2 and 3:
Total number of ways = 10! * 9!
Simplifying this expression, we get:
Total number of ways = 10! * 9! = 10 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1 * 9 * 8 * 7 * 6 * 5 * 4 * 3 * 2 * 1
This simplifies to:
Total number of ways = 9!
Therefore, the correct answer is option B) 756.
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Community Answer
Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pin...
B 9!for all balloons and divided by 5!×2!×2! For same color balloons. The correct answer is (9!)÷(5!×2!×2!)=756?
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Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer?
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Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer?.
Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Sonia has 10 balloons out of which 5 are red, 2 white, 2 blue and 1pink, which she wants to use for the decoration. Her favourite pink colour balloon should be filled with toffees and should be put at the centre of the room above the cake table and remaining 9 at the wall behind the cake table. How many ways she can arrange the balloons?a)956b)756c)9!d)7560Correct answer is option 'B'. Can you explain this answer?.
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