Question
A code word is formed by two distinct English letters followed by two non-zero distinct digits. Find the number of such code words. Also, find the number of such code words that end with an even digit.
(ii) There are total 26 alphabets.
A code word contains 2 English alphabets.
$\therefore 2$ alphabets can be filled in ${ }^{26} \mathrm{P}_2$
$
\begin{aligned}
& =\frac{26}{(26-2) !} \\
& =\frac{26 \times 25 \times 24 !}{24 !} \\
& =650 \text { ways }
\end{aligned}
$
For a code word to end with an even integer, the digit in the unit's place should be an even number between 1 to 9 which can be filled in 4 ways.
Also, 10 's place can be filled in 8 ways.
$\therefore$ Total number of codewords $=650 \times 4 \times 8=20800$ ways
$\therefore 20800$ codewords end with an even integer.
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| football | cricket | Hockey | basketball | |
| Boys | 86 | 60 | 44 | 10 |
| Girls | 40 | 30 | 25 | 5 |
(i) 2x – y + z = 1, x + 2y + 3z = 8, 3x + y – 4z = 1
(i) 2x – y + z = 1, x + 2y + 3z = 8, 3x + y – 4z = 1
| Offered | Denied | |
| Male | 75 | 150 |
| Female | 25 | 50 |