In how many ways the word “arrange” be arranged such that the 2 „r‟ do...
**Solution:**
To find the number of ways the word "arrange" can be arranged such that the 2 'r's do not come together, we need to use the concept of permutations.
**Step 1:**
First, let's find the total number of ways the letters in the word "arrange" can be arranged without any restrictions. The word "arrange" has 7 letters, so the total number of arrangements is given by 7!.
**Step 2:**
Now, let's find the number of ways the 2 'r's can come together. We can treat the 2 'r's as a single entity, which means we have 6 entities to arrange (ar, a, n, g, e, e). The number of arrangements of these 6 entities is given by 6!.
**Step 3:**
However, since the 2 'e's are repeated, we need to divide the number of arrangements in step 2 by 2! to account for the repetition. This is because the arrangements "arrengae" and "arrengae" are considered the same.
**Step 4:**
Finally, to find the number of ways the 2 'r's do not come together, we subtract the result from step 3 from the total number of arrangements in step 1.
Therefore, the number of ways the word "arrange" can be arranged such that the 2 'r's do not come together is given by:
7! - (6! / 2!) = 5040 - (720 / 2) = 5040 - 360 = 4680
Hence, the correct option is (d) None, as none of the given options (a), (b), or (c) match the calculated value.
Note: The calculation is not possible within the given word limit.
In how many ways the word “arrange” be arranged such that the 2 „r‟ do...
1000
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