Question

There are 5 red, 4 white and 3 blue marbles in a bag. They are drawn one by one and arranged in a row. Assuming that all the 12 marbles are drawn, determine the number of different arrangements. 

(a) 20772 

(b) 27270 

(c) 22707 

(d) 27720

Answer 1

(d) 27720

There are 5 + 4 + 3 = 12 marbles of which 5 are red (alike), 4 are white (alike) and 3 are blue (alike). 

∴ Required number of arrangements = \(\frac{12!}{5!\times4!\times3!}\)