Question

How many 4 digit number can be formed using 1,2,3,4,5,6,7 with none of digits being replaced?

Answer 1

hey buddy here is your answer

according to permutation and combination we can do it .

==> we have to make 4 digit number without repetition

==> for this we got (_ _ _ _ ) space to fill
for first space we can fill it by 7 ways because we got all 7 numbers to fill

So 7 ways for first

and for second space we got 6 ways because 1 of 7 numbers we already used of first space so no repetition we got only 6 ways for second space

same for 3rs space we got only 5 choices to make .
so 5 ways for 3rd space

and for last space we got only 4 numbers so only 4 ways for last space

===> in the last total ways for all four spaces is = multiply all possible ways for each space

===> 7(1 space)*6(2nd space )*5(3rd space )*4(4th space = 840 ways ( answer)

there are total 840 ways to fill 4 blanks without repetition

----hope it helps--- ask me if you still got confusion
-- all the best ✌️✌️