SOLUTION: A fashion magazine runs a competition, in which 8 photographs of dresses are shown, lettered A, B, C, D, E, F, G and H. Competitors are asked to submit an arrangement of 5 letters

Question 472796: A fashion magazine runs a competition, in which 8 photographs of dresses are shown, lettered
A, B, C, D, E, F, G and H. Competitors are asked to submit an arrangement of 5 letters
showing their choice of dresses in descending order of merit. The winner is picked at random
from those competitors whose arrangement of letters agrees with that chosen by a panel of
experts.
(i) Calculate the number of possible arrangements of 5 letters chosen from the 8.
Calculate the number of these arrangements
(ii) in which A is placed first,
(iii) which contain A.
*Please answer as soon as possible bro :)
Answer by sudhanshu_kmr(1152) (Show Source): You can put this solution on YOUR website!

(i) Calculate the number of possible arrangements of 5 letters chosen from the 8.
number of arrangements = 8P5 = 8!/3! = 6720

Calculate the number of these arrangements
(ii) in which A is placed first,
number of arrangements = 7P4 = 7!/3! = 840

(iii) which contain A.
number of ways to select another 4 letters (excluding A) = 7C4 = 35
number of ways to arrange these 5 ( including A) = 5! = 120
total possible arrangement that contains A = 120*35 = 4200

if any doubt, you are welcome to ask ...
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