Each of 10 letters A,H,I,M,O,T,U,V,W and X appears same when looked at in a mirror. They are called

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6.Permutation and Combination

normal

Each of the $10$ letters $A,H,I,M,O,T,U,V,W$ and $X$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letters computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?

$720$

$12240$

$3360$

$14880$

Solution

$\left( \,\underset{Total\,\,\operatorname{se}lections}{\mathop{^{26}{{C}_{3}}}}\,-\,\underset{\begin{smallmatrix}
\operatorname{se}lection\,\,excluding \\
symmetric\,\,letters
\end{smallmatrix}}{\mathop{^{16}{{C}_{3}}}}\, \right)\times 3!=12240$

Standard 11

Mathematics

In a shop there are five types of ice-creams available. A child buys six ice-creams.

Statement $-1 :$ The number of different ways the child can buy the six ice-creams is $^{10}C_5.$

Statement $-2 :$ The number of different ways the child can buy the six ice-creams is equal to the number of different ways of arranging $6 \,A's$ and $4 \,B's$ in a row.

hard

(AIEEE-2008)

${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:

hard

(JEE MAIN-2024)

In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is

easy

The solution set of $^{10}{C_{x – 1}} > 2\;.{\;^{10}}{C_x}$ is

easy

Suppose Anil's mother wants to give $5$ whole fruits to Anil from a basket of $7$ red apples, $5$ white apples and $8$ oranges. If in the selected $5$ fruits, at least $2$ orange, at least one red apple and at least one white apple must be given, then the number of ways, Anil's mother can offer $5$ fruits to Anil is $……..$

hard

(JEE MAIN-2023)

Each of the $10$ letters $A,H,I,M,O,T,U,V,W$ and $X$ appears same when looked at in a mirror. They are called symmetric letters. Other letters in the alphabet are asymmetric letters. How many three letters computer passwords can be formed (no repetition allowed) with at least one symmetric letter ?

Solution

Similar Questions

${ }^{n-1} C_r=\left(k^2-8\right){ }^n C_{r+1}$ if and only if:

In an examination there are three multiple choice questions and each question has $4 $ choices. Number of ways in which a student can fail to get all answers correct, is

The solution set of $^{10}{C_{x – 1}} > 2\;.{\;^{10}}{C_x}$ is

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