Question

Find the number of ways of arranging the letters of the word ramanujan so that the relative position of vowels and consonants are not changed

Answer 1

Answer:

240

Step-by-step explanation:

the relative position of vowels and consonants are not changed

so  no of ways  that vowels can be arranged = 4!/3! = 4  

                                                                     [ 3 a are there ]

no of ways  that   consonants can be arranged =5!/2! =5x4x3 =60  

                                                                    [  2 n are there ]

total arrangement 4 x60= 240

Answer 2

$\large\bold{\underline{\underline{Answer :-}}}$

$\sf{\ In \: the \: word \: RAMANUJAN \: there \: are \: 4 \: vowels \: (A, A, U, A) \: in \: that \: 3 \: A's, \: 1 U \: and \: 5 \: Constants \: (R, M, N, J, N) in \: that \: two \: N's \: and \: rest \:are distinct.}$

$\sf{\ The \: 4 \: Vowels \: (A, A, A, U) \: can \: be \: arranged \: themselves \: in \: \frac{4! }{3!} = 4 \: ways}$

$\sf{\ The \: 5 \: Constants \: (R, M, N, J, N) \: can \: be \: arranged \: themselves \: in \: \frac{5! }{2! } = 60 \: ways}$

$\sf{\ ∴Therefore \: the \: number \: of \: required \: arrangements \: are \: \frac{4! }{3! } \times \frac{5! }{2! } = 4 \times 60 = 240}$