Cargo returns error: no default toolchain configured

Hi I'm an absolute noob
and I'm trying to get started with Rust
I'm on Ubuntu 18.04 I run in terminal
curl --proto '=https' --tlsv1.2 -sSf https://sh.rustup.rs | sh
it failed to add ~/.cargo/bin to $PATH

error: could not amend shell profile: '/home/francesco/.bash_profile'
error: caused by: could not write rcfile file: '/home/francesco/.bash_profile'
error: caused by: Permission denied (os error 13)

so I did it myself,
and which rustup returns /home/francesco/.cargo/bin/rustup
rustup --version returns rustup 1.21.1 (7832b2ebe 2019-12-20)
which cargo returns /home/francesco/.cargo/bin/cargo

but...
~/projects$ cargo new hello returns error: no default toolchain configured
same for cargo --version , which rustc and rustc --version.

What did I miss?
Thanks in advance

Try running

rustup default stable

if that doesn't help, try reinstalling, but this time with acceptable permissions from the start. Perhaps it aborted before finishing the setup.

Try the --no-modify-path flag of rustup-init.

francesco@francesco-yoga720:~$ rustup default stable
info: syncing channel updates for 'stable-x86_64-unknown-linux-gnu'
info: latest update on 2020-01-30, rust version 1.41.0 (5e1a79984 2020-01-27)
info: downloading component 'cargo'
  4.7 MiB /   4.7 MiB (100 %) 665.6 KiB/s in  7s ETA:  0s
info: downloading component 'clippy'
  1.8 MiB /   1.8 MiB (100 %) 429.4 KiB/s in  4s ETA:  0s
info: downloading component 'rust-docs'
 12.0 MiB /  12.0 MiB (100 %)   1.1 MiB/s in 17s ETA:  0s
info: downloading component 'rust-std'
 17.5 MiB /  17.5 MiB (100 %) 686.6 KiB/s in 26s ETA:  0s
info: downloading component 'rustc'
 57.9 MiB /  57.9 MiB (100 %)   1.0 MiB/s in  1m 18s ETA:  0s
info: downloading component 'rustfmt'
  3.1 MiB /   3.1 MiB (100 %) 1018.2 KiB/s in  3s ETA:  0s
info: installing component 'cargo'
info: installing component 'clippy'
info: installing component 'rust-docs'
 12.0 MiB /  12.0 MiB (100 %)   9.0 MiB/s in  1s ETA:  0s
info: installing component 'rust-std'
 17.5 MiB /  17.5 MiB (100 %)  16.4 MiB/s in  1s ETA:  0s
info: installing component 'rustc'
 57.9 MiB /  57.9 MiB (100 %)  11.7 MiB/s in  5s ETA:  0s
info: installing component 'rustfmt'
info: default toolchain set to 'stable-x86_64-unknown-linux-gnu'

  stable-x86_64-unknown-linux-gnu installed - rustc 1.41.0 (5e1a79984 2020-01-27)

francesco@francesco-yoga720:~$ which rustc
/home/francesco/.cargo/bin/rustc
francesco@francesco-yoga720:~$ rustc --version
rustc 1.41.0 (5e1a79984 2020-01-27)
francesco@francesco-yoga720:~$ cd projects
francesco@francesco-yoga720:~/projects$ cargo new hello
     Created binary (application) `hello` package
francesco@francesco-yoga720:~/projects$ 

everything looks fine now
thank you @kornel

the issue can be closed