Answer:
331776
Step-by-step explanation:
Since n? = n! · (n − 1)! · … · 1! And n# = n? · (n − 1)? · … · 1?
Then 4# = 4? · (4 − 1)? · (4 − 2)?· 1?
= 4? · 3? · 2?· 1?
Now, n? = n! · (n − 1)! · … · 1!
So, 4? = 4! · (4 − 1)! · (4 − 2)! · 1! = 4! · 3! · 2! · 1! = 288
Thus, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12
Also, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2
and 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1
So, 4# = 4? · 3? · 2?· 1? = 288 × 12 × 2 × 1 = 6912
We now find 3#
3# = 3? · (3 − 1)? · 1? = 3? · 2?· 1?
Now, n? = n! · (n − 1)! · … · 1!
So, 3? = 3! · (3 − 1)! · 1! = 3! · 2! · 1! = 12
Thus, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2
and, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1
So, 3# = 3? · 2?· 1? = 12 × 2 × 1 = 24
We now find 2#
2# = 2? · (2 − 1)? · 1? = 2? · 1?· 1?
Now, n? = n! · (n − 1)! · … · 1!
So, 2? = 2! · (2 − 1)! · 1! = 2! · 1! · 1! = 2
1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1
So, 2# = 2?· 1? = 2 × 1 = 2
We now find 1#
1# = 1? · 1? = 1? · 1?
Now, n? = n! · (n − 1)! · … · 1!
So, 1? = 1! · (1 − 1)! · 1! = 1! · 0! · 1! = 1
And, 1# = 1? · 1? = 1 × 1 = 1
So, 4# · 3# · 2# · 1#? = 6912 · 24 · 2 · 1? = 331776
