In how many ways can arrange the letters of the words ALLAHABAD?1. 302

1.	In how many ways can arrange the letters of the words ALLAHABAD?1. 30242. 50403. 75604. None of these
Answer» Correct Answer - Option 3 : 7560 Given: The word ALLAHABAD Formulaused: When alphabets are repeated then we use this formula The number of ways = n!/(p! q! r!) n→ Total number of alphabets p → First type repeated alphabets q→ Second type repeated alphabets r→ Third type repeated alphabets Calculation: In the word ALLAHABAD n = 9→ total letters in ALLAHABAD p = 4→ number of A's q = 2→ number of L's Put values inthe formula ⇒ The number ofarrangements = 9!/(4! × 2!) ⇒ The number ofarrangements = (9× 8× 7× 6× 5 × 4!)/{(2× 1)4!} ⇒ The number ofarrangements = (9× 8× 7× 6× 5 )/2 ⇒ The number ofarrangements = 7560 ∴ Word ALLAHABAD can arrange 7560 ways.

In how many ways can arrange the letters of the words ALLAHABAD?1. 30242. 50403. 75604. None of these

Answer» Correct Answer - Option 3 : 7560

Given:

The word ALLAHABAD

Formulaused:

When alphabets are repeated then we use this formula

The number of ways = n!/(p! q! r!)

n→ Total number of alphabets

p → First type repeated alphabets

q→ Second type repeated alphabets

r→ Third type repeated alphabets

Calculation:

In the word ALLAHABAD

n = 9→ total letters in ALLAHABAD

p = 4→ number of A's

q = 2→ number of L's

Put values inthe formula

⇒ The number ofarrangements = 9!/(4! × 2!)

⇒ The number ofarrangements = (9× 8× 7× 6× 5 × 4!)/{(2× 1)4!}

⇒ The number ofarrangements = (9× 8× 7× 6× 5 )/2

⇒ The number ofarrangements = 7560

∴ Word ALLAHABAD can arrange 7560 ways.

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