henrymba2021 wrote:
In how many different ways can the letters A, A, B, B, B, C, D, E be arranged if the letter C must be to the right of the letter D?
a. 1,680
b. 2,160
c. 2,520
d. 3,240
e. 3,360
These are the arrangements possible where letter C is to the right of D
D******C
D*****C*
D****C**
D***C***
D**C****
D*C*****
DC******(7 combinations when D is the first alphabet)
*D*****C
*D****C*
*D***C**
*D**C***
*D*C****
*DC*****(6 combinations when D is the second alphabet)
**D****C
**D***C*
**D**C**
**D*C***
**DC****(5 combinations when D is the third alphabet)
The total arrangements possible are \(7+6+5+4+3+2+1 = 28\)
The total ways in which alphabets A,A,B,B,B,C can be arranged are\(\frac{6!}{2!*3!} = \frac{6*5*4*3*2}{2*3*2} = 6*5*2 = 60\)
Therefore, the total ways in which the alphabets can be arranged when C is to the right of D is 28*60 =
1680(Option A)
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