How many ways are there to arrange the letters in the word $$GARDEN$$ with vowels in alphabetical order
A.
480
B.
240
C.
360
D.
120
Answer :
360
Solution :
Total number of arrangements of letters in the word $$GARDEN = 6 ! = 720$$ there are two vowels $$A$$ and $$E,$$ in half of the arrangements $$A$$ preceeds $$E$$ and other half $$A$$ follows E.
So, vowels in alphabetical order in $$\frac{1}{2} \times 720 = 360$$
Releted MCQ Question on Algebra >> Permutation and Combination
Releted Question 1
$$^n{C_{r - 1}} = 36,{\,^n}{C_r} = 84$$ and $$^n{C_{r + 1}} = 126,$$ then $$r$$ is:
Ten different letters of an alphabet are given. Words with five letters are formed from these given letters. Then the number of words which have at least one letter repeated are
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one chair each. First the women choose the chairs from amongst the chairs marked 1 to 4 ; and then the men select the chairs from amongst the remaining. The number of possible arrangements is