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Answer :
20,160 distinct 6-letter words can be formed from the letters of 'TRIANGLE', Thus, the correct answer is between 20,000 and 30,000. Option d.
The word TRIANGLE consists of 8 distinct letters. To find the number of distinct 6-letter words that can be formed from these 8 letters, we use permutations.
We can choose 6 letters out of 8 in 8P6 ways, where ⁿPk = n! / (n-k)!
Thus, 8P6 = 8! / (8-6)! = 8! / 2! = (8 × 7 × 6 × 5 × 4 × 3) = 20160.
So, the number of distinct 6-letter words is 20,160.
Therefore, the correct answer is: d. between 20000 and 30000.
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The number of distinct 6-letter words that can be formed from the letters of the word TRIANGLE is 20,160, which falls into the range of 10,000 and 20,000. The correct option is C.
The question asks for the number of distinct 6-letter words that can be formed with the letters of the word TRIANGLE. This is a problem of permutations without repetition since each letter can be used only once. To solve this, we calculate the number of permutations of 6 letters chosen from the 8 distinct letters of the word TRIANGLE.
The formula for permutations without repetition is P(n, k) = n! / (n - k)!, where n is the total number of items to choose from, k is the number of items to choose, and '!' denotes factorial.
For the word TRIANGLE, n = 8 and k = 6, so the calculation is:
P(8, 6) = 8! / (8 - 6)! = 8! / 2! = 40,320 / 2 = 20,160.
Since 20,160 is between 10,000 and 20,000, the correct answer is (c) between 10000 and 20000 distinct 6-letter words can be formed.
