Question

The number of five digit numbers that can be made with the digits $1,2,3,4,5,6$ in which at least two digits are identical is

• A. $2502$
• B. $6240$
• C. $5261$
• D. $5226$

Answer 1

The correct option is B $6240$

Given digits are $1,2,3,4,5,6$

Required numbers are $5$ digited

(1) $4$ Has to be selected and one is repeated

Total numbers will be

${}^6{C}_4\times 5!=15\times 120=1800$

(2) $3$ has to be selected

${}^6{C}_3\times 5!=20\times 120=2400$

(3) $2$ has to be selected

${}^6{C}_2\times 5!=15\times 120=1800$

(4) $1$ has to be selected

${}^6{C}_1\times 5!=6\times 120=240$

Total $6240$

Hence the correct answer is $6240$