How many different 10 letter words real or imaginary can be formed from the following letters mfnoceffbd?

To find out how many different 10-letter words can be formed from the letters ‘mfnoceffbd’, we first need to look at the letters available and the repetitions among them. The letters we have are:

• m
• f

(2 times)

• n
• o
• c
• e
• b
• d

In total, we have 10 letters, with the letter ‘f’ repeating twice. The formula to calculate the number of different arrangements of letters, where some letters may be identical, is given by:

Number of arrangements = n! / (p1! * p2! * … * pk!)

Where n is the total number of letters, and p1, p2, …, pk are the counts of each identical letter. Here, we have:

• n = 10 (total letters)
• p1 = 2! (for ‘f’)

Now we’ll calculate it:

Number of arrangements = 10! / (2!)

10! = 3628800

And, 2! = 2

So we get:

Number of arrangements = 3628800 / 2 = 1814400

Therefore, the total number of different 10-letter words, real or imaginary, that can be formed from the letters ‘mfnoceffbd’ is 1,814,400.