JEE MAIN - Mathematics (2020 - 8th January Evening Slot - No. 2)
The number of 4 letter words (with or without
meaning) that can be formed from the eleven
letters of the word 'EXAMINATION' is
_______.
Answer
2454
Explanation
2A, 2I, 2N, E, X, M, T, O
To form four letter words
Case 1 : All same ( not possible)
Case 2 : 1 different, 3 same (not possible)
Case 3 : 2 different, 2 same
= 3C1 $$ \times $$ 7C2 $$ \times $$ $${{4!} \over {2!}}$$ = 756
Case 4 : 2 same of one kind, 2 same same of other kind
= 3C2 $$ \times $$ $${{4!} \over {2!2!}}$$ = 18
Case 5 : All letters are different
= 8C4 $$ \times $$ 4! = 1680
$$ \therefore $$ Total ways = 1680 + 756 + 18 = 2454
To form four letter words
Case 1 : All same ( not possible)
Case 2 : 1 different, 3 same (not possible)
Case 3 : 2 different, 2 same
= 3C1 $$ \times $$ 7C2 $$ \times $$ $${{4!} \over {2!}}$$ = 756
Case 4 : 2 same of one kind, 2 same same of other kind
= 3C2 $$ \times $$ $${{4!} \over {2!2!}}$$ = 18
Case 5 : All letters are different
= 8C4 $$ \times $$ 4! = 1680
$$ \therefore $$ Total ways = 1680 + 756 + 18 = 2454
Comments (0)
