The number of ways in which 5 differently colored flags can be arranged in arrow areA.50B.120C.180D.100
Question
The number of ways in which 5 differently colored flags can be arranged in arrow areA.50B.120C.180D.100
Solution 1
To find the number of ways in which 5 differently colored flags can be arranged in an arrow, we can use the concept of permutations.
Step 1: Determine the number of positions for the first flag. Since it is an arrow, there is only one position for the first flag.
Step 2: Determine the number of positions for the second flag. Since the first flag has already been placed, there are 4 remaining positions for the second flag.
Step 3: Determine the number of positions for the third flag. Since the first and second flags have already been placed, there are 3 remaining positions for the third flag.
Step 4: Determine the number of positions for the fourth flag. Since the first, second, and third flags have already been placed, there are 2 remaining positions for the fourth flag.
Step 5: Determine the number of positions for the fifth flag. Since the first, second, third, and fourth flags have already been placed, there is only 1 remaining position for the fifth flag.
To find the total number of arrangements, we multiply the number of positions for each flag together:
1 * 4 * 3 * 2 * 1 = 24
Therefore, there are 24 different ways in which 5 differently colored flags can be arranged in an arrow.
None of the given options (A. 50, B. 120, C. 180, D. 100) match the correct answer.
Solution 2
To find the number of ways in which 5 differently colored flags can be arranged in an arrow, we can use the concept of permutations.
Step 1: Determine the number of positions for the first flag. Since it is an arrow, there is only one position for the first flag.
Step 2: Determine the number of positions for the second flag. Since the first flag has already been placed, there are 4 remaining positions for the second flag.
Step 3: Determine the number of positions for the third flag. Since the first and second flags have already been placed, there are 3 remaining positions for the third flag.
Step 4: Determine the number of positions for the fourth flag. Since the first, second, and third flags have already been placed, there are 2 remaining positions for the fourth flag.
Step 5: Determine the number of positions for the fifth flag. Since the first, second, third, and fourth flags have already been placed, there is only 1 remaining position for the fifth flag.
To find the total number of arrangements, we multiply the number of positions for each flag together:
1 * 4 * 3 * 2 * 1 = 24
Therefore, there are 24 different ways in which 5 differently colored flags can be arranged in an arrow.
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