how many inventions/preludes did bach write?

Answer 1

I assume you mean Johann Sebastian Bach:
A bunch:

The Well-Tempered Clavier (846–893)
BWV 846 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 1 in C major
BWV 846a — Prelude and Fugue in C major (alternative version of BWV 846)
BWV 847 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 2 in C minor
BWV 848 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 3 in C-sharp major
BWV 849 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 4 in C-sharp minor
BWV 850 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 5 in D major
BWV 851 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 6 in D minor
BWV 852 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 7 in E-flat major
BWV 853 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 8 in E-Flat minor
(The Fugue of this work is actually in D-sharp minor, the enharmonic key of E-flat minor)
BWV 854 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 9 in E major
BWV 855 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 10 in E minor
BWV 855a — Prelude and Fugue in E minor (alternative version of BWV 855)
BWV 856 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 11 in F major
BWV 857 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 12 in F minor
BWV 858 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 13 in F-sharp major
BWV 859 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 14 in F-sharp minor
BWV 860 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 15 in G major
BWV 861 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 16 in G minor
BWV 862 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 17 in A-flat major
BWV 863 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 18 in G-sharp minor
BWV 864 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 19 in A major
BWV 865 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 20 in A minor
BWV 866 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 21 in B-flat major
BWV 867 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 22 in B-flat minor
BWV 868 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 23 in B major
BWV 869 — Well-Tempered Clavier, Book 1: Prelude and Fugue No. 24 in B minor
BWV 870 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 1 in C major
BWV 870a — Prelude and Fugue in C major (alternative version of BWV 870)
BWV 870b — Prelude in C major (alternative version of BWV 870)
BWV 871 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 2 in C minor
BWV 872 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 3 in C-sharp major
BWV 872a — Prelude and Fugue in C-sharp major (alternative version of BWV 872)
BWV 873 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 4 in C-sharp minor
BWV 874 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 5 in D major
BWV 875 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 6 in D minor
BWV 875a — Prelude in D minor (alternative version of BWV 875)
BWV 876 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 7 in E-flat major
BWV 877 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 8 in D-sharp minor
BWV 878 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 9 in E major
BWV 879 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 10 in E minor
BWV 880 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 11 in F major
BWV 881 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 12 in F minor
BWV 882 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 13 in F-sharp major
BWV 883 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 14 in F-sharp minor
BWV 884 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 15 in G major
BWV 885 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 16 in G minor
BWV 886 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 17 in A-flat major
BWV 887 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 18 in G-sharp minor
BWV 888 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 19 in A major
BWV 889 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 20 in A minor
BWV 890 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 21 in B-flat major
BWV 891 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 22 in B-flat minor
BWV 892 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 23 in B major
BWV 893 — Well-Tempered Clavier, Book 2: Prelude and Fugue No. 24 in B minor
[edit]
Preludes and fugues, toccatas and fantasias (894–923)
BWV 894 — Prelude and Fugue in A minor
BWV 895 — Prelude and Fugue in A minor
BWV 896 — Prelude and Fugue in A major
BWV 897 — Prelude and Fugue in A minor
BWV 898 — Prelude and Fugue in B-flat major on the name B-A-C-H (doubtful)
BWV 899 — Prelude and Fughetta in D minor
BWV 900 — Prelude and Fughetta in E minor
BWV 901 — Prelude and Fughetta in F major
BWV 902 — Prelude and Fughetta in G major
BWV 902a — Prelude in G major (alternative version of BWV 902)

Please go to the links below for complete listings