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:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → Both (A) and (B)
\(n\) different letters can be arranged in \(n!\) ways. When some letters must go into certain places, those places are filled first and the rest of the letters go into the remaining places.
(A) The different ways in which the alphabets of the word BAKERY can be arranged is 720 Correct. BAKERY has 6 letters, all different, so they can be arranged in \(6!=720\) ways.
(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 Correct. MACHINE has 7 different letters: 3 vowels (A, I, E) and 4 consonants (M, C, H, N). The odd positions are 1, 3, 5 and 7.
Vowels into 3 of the 4 odd positions: \(4\times3\times2=24\) ways
Consonants into the 4 places left: \(4!=24\) ways
Total \(=24\times24=576\)