KarishmaB - here is how I approached the question. Can you please let me know what I am missing in the first approach-
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FirstApproach : Using Probability
Step 1: Fill the last digit - To obtain a range of 7, we must have either 10, 9 or 8 in the last digit. The probability of getting a 10, 9 or 8 in the last digit = 3/10
Step 2: Fill the first digit - The first digit can be filled only in 1 way. The probability of getting that digit = 1/9
Step 3: The middle two digits can be filled in 6 ways and 5 ways respectively. Their probability = 6/8 * 5/7
Step 4: The four numbers can be arranged in 4! ways
Total Probability = 3/10 * 1/9 * 6/8 * 5/7 * 4 ! = 3/7
Not sure what I am missing here.
SecondApproach : Using Filling Space Method
Step 1: Fill the last digit - To obtain a range of 7, we must have either 10, 9 or 8 in the last digit. Hence, the last digit can be filled in 3 ways.
Step 2: Fill the first digit - The first digit can be filled only in 1 way.
Step 3: The middle
...
_ _ __
FirstApproach : Using Probability
Step 1: Fill the last digit - To obtain a range of 7, we must have either 10, 9 or 8 in the last digit. The probability of getting a 10, 9 or 8 in the last digit = 3/10
Step 2: Fill the first digit - The first digit can be filled only in 1 way. The probability of getting that digit = 1/9
Step 3: The middle two digits can be filled in 6 ways and 5 ways respectively. Their probability = 6/8 * 5/7
Step 4: The four numbers can be arranged in 4! ways
Total Probability = 3/10 * 1/9 * 6/8 * 5/7 * 4 ! = 3/7
Not sure what I am missing here.
SecondApproach : Using Filling Space Method
Step 1: Fill the last digit - To obtain a range of 7, we must have either 10, 9 or 8 in the last digit. Hence, the last digit can be filled in 3 ways.
Step 2: Fill the first digit - The first digit can be filled only in 1 way.
Step 3: The middle
...
Statistics : Posted by GMATCenturion • on 19 May 2019, 12:05 • Replies 10 • Views 9611
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