Airtable doesn't currently offer a formula to count the number of selected options. However, if you convert the multi-select field into a linked records field (choose the "Create new table" option when doing so), you can then use a COUNT field to return the number of selected linked records.
Another option is to use a formula workaround as below:
IF({YOUR MULTIPLE-SELECT FIELD NAME},LEN({YOUR MULTIPLE-SELECT FIELD NAME})-LEN(SUBSTITUTE({YOUR MULTIPLE-SELECT FIELD NAME},",",""))+1)
**Only caveat to the above formula is that none of the multi-select field options can have an embedded comma.