Find number of ways of selection of one or more letters from AAAABBCCCDEF
(i) there is no restriction.
(ii) the letters A & B are selected atleast once.
(iii) only one letter is selected.
(iv) atleast two letters are selected
Text Solution
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(i) AAAABBCCCDEF
A → 4
B → 2
C → 3 (4 + 1) (2 + 1) (3 + 1) (1 + 1) (1 + 1) (1 + 1) – 1 = 5 . 3 . 4 . 2 . 2 . 2 – 1 = 480 – 1 = 479
D → 1
E → 1
F → 1
(ii) A → 3
B → 1
C → 3 (3 + 1) (1 + 1) (3 + 1) (1 + 1) (1 + 1) (1 + 1) = 16 × 16 = 256
D → 1
E → 1
F → 1
(iii) Only one letter selected 6 C 1 = 6
(iv) Atleast two letters selected =Total–(no letter is selected)–(One letter selected) = 480–1– 6= 473
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