(A) $5$-digit telephone number starts with $67$. This means the first two places are fixed as $6$ and $7$. Since no digit can be repeated,we have $10

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(A) $5$-digit telephone number starts with $67$. This means the first two places are fixed as $6$ and $7$. Since no digit can be repeated,we have $10 - 2 = 8$ digits remaining to fill the remaining $3$ places. The third place can be filled in $8$ ways. The fourth place can be filled in $7$ ways. The fifth place can be filled in $6$ ways. By the multiplication principle,the total number of such telephone numbers is $8 \times 7 \times 6 = 336$.

Class 11 Mathematics Permutation and Combination Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

A
$336$
B
$338$
C
$340$
D
$342$

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Permutation and Combination

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Definition of permutation, Number of permutations with or without repetition, Conditional permutations

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How many $5$-digit telephone numbers can be constructed using the digits $0$ to $9$ if each number starts with $67$ and no digit appears more than once?

Similar Questions

How many $8$-digit numbers can be formed such that all digits are distinct?

If the number of words,with or without meaning,which can be made using all the letters of the word $MATHEMATICS$ in which $C$ and $S$ do not come together,is $(6 !) k$,then $k$ is equal to $............$.

The number of arrangements of the letters of the word $ARRANGEMENT$ in which two $E$s do not occur adjacently is

How many $5$-digit numbers can be formed without any conditions?

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