Math, asked by swapnajitrock7818, 1 year ago

Using an alphabet of 26 letters, how many sets of initials can be formed if every person has exactly one first name and one surname (last name)

Answers

Answered by Ashi03
0
(i) There are 26 possible letters, each set of initials would have 3 letters in it, order doesnt matter, i.e. ABC does not equal ACB. So type in 26P3 on your calculator (P=permutation).

(ii) This time each set of initials can have 2 or 3 values, so calculate 26P3 + 26P2.

(iii) 26P4 + 26P3 + 26P2.

(iv) x = solution for (ii) - 20,000

Hope this helps...
Answered by lucky1829
0
The number of initials made from people whose full name includes three names is 26*26*26 = 17,576. For four names, it's 26^4 = 456,976. 

Assuming that everybody has at least one middle name and thus only 3 or 4 initials, then there can be no more than 17,576 people with unique sets of 3 initials. Which means either some of those 20,000 have repeating initials, or at least 20,000-17576 = 2,424 people must have more than three initials.
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