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)
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(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...
(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...
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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.
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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