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The number of 4 letter words (with or without meaning) that ca

Question

The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word
'EXAMINATION' is _______

2454

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The number of

4

letter words (with or without meaning) that can be formed from the eleven letters of the word
'EXAMINATION' is _______

11 mins ago

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11 mins ago

Text solutionVerified

EX A M I N A T I ON

N - 2

A - 2

I - 2

E - 1

X - 1

M - 1

T - 1

O - 1

Case I All different

=^{8} C_{4} 4! = 1680

Case II 2 same 2 different

= 3 C_{1}^{7} C_{2} \frac{4 !}{2 !} = 3 \times 21 \times 12 = 756

Case III 2 same 2 other same

=^{3} C_{2} \times \frac{4 !}{2 ! 2 !} = 3 \times 6 = 18

∴

Total

= 1680 + 756 + 18

= 2454

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Question Text	The number of $4$ letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is _______
Answer Type	Text solution:1
Upvotes	151