How many words each of 2 vowels and 3 consonants can be formed using the letters of the word DAUGHTER

ncert cbse 7th chapter permutations miscellaneous exercise

1.How many words each of 2 vowels and 3 consonants can be formed using the letters of the word DAUGHTER

The vowels are A,U,E

We have to select 2 out of the 3 vowels in C(3,2)= [3*2]/[1*2]= 3 ways

The consonants are D,G,H,T,R

We have to select 3 out of the 5 vowels in C(5,3)= [5*4] / [1*2] =10ways

because C(n,r) = C[n,(n-r)]  gives C(5,3)=C(5,2)

now the 2+3= 5 selected letters can be arranged among themselves in

5! =5*4*3*2*1=120 ways

Required number of words = 3*10*120 =3600

2. How many words of can be formed using all the letters of the word

 EQUATION  so that the vowels and consonants occur together?

Vowels are E,U,A,I,O

Treat the 5 vowels as a single unit. Inside this the 5 vowels can be arranged

among themselves in 5!=5*4*3*2*1=120 ways

Consonants are Q,T,N

Treat the 3 consonants as a single unit. Inside this the 3 consonants can be arranged among themselves in 3!=3*2*1=6 ways

Now the two units can be arranged among themselves in 2!=2*1 = 2 ways

Required number of words =120*6*2=1440 words

ncert cbse 11th mathematics chapter  7 permutations exercise 7.3

11.In how many ways can the letters of the word PERMUTATIONS be arranged if

i)words start with P and end with S

ii)vowels are all together

iii)there are always 4 letters between P and S

solution

ncert cbse 11th mathematics chapter  7 permutations miscellaneous exercise

1.How many words each of 2 vowels and 3 consonants can be formed using the letters of the word DAUGHTER

solution

2. How many words of can be formed using all the letters of the word

 EQUATION  so that the vowels and consonants occur together?

solution

4. If the different permutations of the word EXAMINATION are arranged in a dictionary how many words are there in this list before the first word starting with E

solution

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