Read the information given below carefully and answer the question that follows:

(A) The different ways in which the alphabets of the word BAKERY can be arranged is 720

(B) The number of ways in which the alphabets of the word MACHINE can be arranged so that the vowels will occupy only the odd positions is 576

Choose the correct answer from the options given below:

The word BAKERY has 6 letters: B, A, K, E, R, Y

All letters are different with no repetitions.

Number of arrangements $= 6!$

$= 6 \times 5 \times 4 \times 3 \times 2 \times 1$

$= 720$

Statement (A) is correct.

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The word MACHINE has 7 letters: M, A, C, H, I, N, E

Vowels: A, I, E (3 vowels)

Consonants: M, C, H, N (4 consonants)

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In a 7-letter word:

Odd positions: 1, 3, 5, 7 (4 positions)

Even positions: 2, 4, 6 (3 positions)

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The condition requires all vowels to occupy only odd positions.

The 3 vowels must be placed in 3 of the 4 odd positions.

The 4 consonants will occupy the remaining 4 positions (1 odd + 3 even).

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Ways to select 3 odd positions from 4 odd positions:

$\binom{4}{3} = 4$

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Ways to arrange 3 vowels in the selected 3 positions:

$3! = 6$

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Ways to arrange 4 consonants in the remaining 4 positions:

$4! = 24$

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Total arrangements $= 4 \times 6 \times 24$

$= 24 \times 24$

$= 576$

Statement (B) is correct.

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Both statements (A) and (B) are correct.