The number of ways in which any four letters | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(c) Four letters can be selected in the following ways

$(i)$ All different $i.e.$ $C,\;O,\;R,\;G$.

$(ii)$ $2$ like and $2$ different.

$(iii)$

Vedclass · Accepted Answer

$7$

Vedclass · Answer

(c) Four letters can be selected in the following ways

$(i)$ All different $i.e.$ $C,\;O,\;R,\;G$.

$(ii)$ $2$ like and $2$ different.

$(iii)$ $3$ like and $1$ different

$i.e.$ three $O$ and $1$ from $R$, $G$ and $C$.

The number of ways in $(i)$ is $^4{C_4} = 1$

The number of ways in $(ii)$ is $1\;.{\;^3}{C_2} = 3$

The number of ways in $(iii)$ is $1{ 	imes ^3}{C_1} = 3$

Therefore, required number of ways = $1 + 3 + 3 = $7.

The number of ways in which any four letters can be selected from the word ‘$CORGOO$’ is

Similar Questions

If $n$ and $r$ are two positive integers such that $n \ge r,$ then $^n{C_{r - 1}}$$ + {\,^n}{C_r} = $

Let $A = \left\{ {{a_1},\,{a_2},\,{a_3}.....} \right\}$ be a set containing $n$ elements. Two subsets $P$ and $Q$ of it is formed independently. The number of ways in which subsets can be formed such that $(P-Q)$ contains exactly $2$ elements, is

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 ?

If $^n{C_3} + {\,^n}{C_4} > {\,^{n + 1}}{C_3},$ then

$\mathop \sum \limits_{0 \le i < j \le n} i\left( \begin{array}{l}
n\\
j
\end{array} \right)$ is equal to