CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

How many different words can be formed using all the letters of the word $$'COMBINATION'$$ such that the vowels as well as consonants appear in alphabetical order?


A
426
loader
B
462
loader
C
624
loader
D
None of the above
loader

Solution

The correct option is B $$462$$
Given letters $$C,O,O,M,B,I,I,N,N,A,T$$
Consonants $$- \;C,M,B,N,N,T=6$$ letters
Vowels $$-\;O,O,I,I,A=5$$ letters
Total permutations of the given word is equal to $$\dfrac{11!}{2!2!2!}$$
Total no. of arrangements of consonants $$=\dfrac{6!}{2!}=360$$
Out of these $$360$$ ways , only one way has the alphabets in the order $$B,C,M,N,N,T$$ ( alphabetical )
Similarily for vowels  total $$=\dfrac{5!}{2!2!}=30$$
Only one of $$30$$ has the alphabets in the order $$A,I,I,O,O$$
$$\therefore$$ By symmetry the arrangements of given word with consonants and vowels in alphabetical order is $$\dfrac{1}{360}\times \dfrac{1}{30} \times \dfrac{11!}{2!2!2!}=462$$
Hence, the answer is $$462.$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image