Question

Find number of ways of selection of one or more letters from AAAABBCCCDEF only one letter selected

Answer 1

Step-by-step explanation:

$ANSWER</p><p></p><p>There are 4 A, 2 B, 3 C 1 D, 1 E and 1 F then</p><p></p><p></p><p>i) Total number of letters =12</p><p></p><p>Number of ways of selection of one or more letters =12c1+12c2+......+12c12=∑r=11212cr.</p><p></p><p></p><p>ii) There are 4 ways of selecting A.</p><p></p><p>There are 2 ways of selecting B.</p><p></p><p>There are 4 ways of selecting C as we select either 1 C, or 2 C or 3 C or we don't choose C.</p><p></p><p>There are 2 ways of selecting D as we select either 1 D or we don't choose D.</p><p></p><p>There are 2 ways of selecting E as we select either 1 E or we don't choose E.</p><p></p><p>There are 2 ways of selecting F as we select either 1 F or we don't choose F.</p><p></p><p></p><p>Hence the total possible ways =4×2×4×2×2×2=256.</p><p></p><p>$

Answer 2

Answer:

There are 4 A, 2 B, 3 C 1 D, 1 E and 1 F then

i) Total number of letters =12

Number of ways of selection of one or more letters =

12

c

1

+

12

c

2

+......+

12

c

12

=∑

r=1

12

12

c

r

.

ii) There are 4 ways of selecting A.

There are 2 ways of selecting B.

There are 4 ways of selecting C as we select either 1 C, or 2 C or 3 C or we don't choose C.

There are 2 ways of selecting D as we select either 1 D or we don't choose D.

There are 2 ways of selecting E as we select either 1 E or we don't choose E.

There are 2 ways of selecting F as we select either 1 F or we don't choose F.

Hence the total possible ways =4×2×4×2×2×2=256.