(A) The total number of four-letter words that can be formed using $26$ letters is $26^4 = 456976$.The number of four-letter words formed using only l

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(A) The total number of four-letter words that can be formed using $26$ letters is $26^4 = 456976$.The number of four-letter words formed using only letters from set $V$ (vowels) is $5^4 = 625$.The number of four-letter words formed using only letters from set $C$ (consonants) is $21^4 = 194481$.The number of words containing at least one vowel and at least one consonant is given by the total number of words minus the words containing only vowels and the words containing only consonants.Number of words $= 26^4 - 5^4 - 21^4$$= 456976 - 625 - 194481$$= 261870$.

Class 11 Mathematics Sets Word Problem - Set Theory

Difficult

Let $E$ denote the set of letters of the English alphabet,$V = \{a, e, i, o, u\}$ and $C$ be the complement of $V$ in $E$. Then,the number of four-letter words (where repetitions of letters are allowed) having at least one letter from $V$ and at least one letter from $C$ is

KVPY 2019 All KVPY

A
$261870$
B
$314160$
C
$425880$
D
$851760$

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Let $E$ denote the set of letters of the English alphabet,$V = \{a, e, i, o, u\}$ and $C$ be the complement of $V$ in $E$. Then,the number of four-letter words (where repetitions of letters are allowed) having at least one letter from $V$ and at least one letter from $C$ is

Similar Questions

In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student has opted for neither $NCC$ nor $NSS$.

In a survey of $60$ people,it was found that $25$ people read newspaper $H$,$26$ read newspaper $T$,$26$ read newspaper $I$,$9$ read both $H$ and $I$,$11$ read both $H$ and $T$,$8$ read both $T$ and $I$,and $3$ read all three newspapers. Find the number of people who read exactly one newspaper.

There are $200$ individuals with a skin disorder. $120$ had been exposed to the chemical $C_{1}$,$50$ to chemical $C_{2}$,and $30$ to both the chemicals $C_{1}$ and $C_{2}$. Find the number of individuals exposed to chemical $C_{1}$ or chemical $C_{2}$.

Let $\bigcup_{i=1}^{50} X_{i} = \bigcup_{i=1}^{n} Y_{i} = T$,where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of the sets $X_{i}$ and exactly $6$ of the sets $Y_{i}$,then $n$ is equal to:

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