The formula for the Stirling number of second kind, the number of partitions of n objects into n-4 boxed is given by the formula. What is (A+B+C)/D?

geduiwelh

geduiwelh

Answered question

2021-08-10

This is for Discrete Math.
The formula for the Stirling number of second kind, the number of partitions of n objects into n-4 boxed is given by the formula
n5+An4n42+Bn3n33+Cn3n32n52+Dn2n22n42n62
What is A+B+CD?
1) 46
2) 6
3) 48
4) 120
5) 24

Answer & Explanation

doplovif

doplovif

Skilled2021-08-11Added 71 answers

Step 1

The formula of Stirling's number for second kind for the number of partitions of n objects into n-4 objects is given by the formula,

S(n,n4)=n5+n4n42+12n3n33+12n3n32n52+14!n2n22n42n62
Now the given formula is,

Equating the two formulae, we get that
A=1,B=12,C=12,D=14!
Step 2
Then the value of A+B+CD is given by
A+B+CD=1+12+1214!
=2×4!
=48
Hence the answer is 48.

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