Although Elton and Lady Gaga performed together, and Elton and Tony performed together, and Tony and Lady Gaga performed together, sadly they never appeared together as a trio. But at least that does give us a total of 3 duets combinations.

But how many duets, everyone asks, could we have if we selected Elton, Tony, Lady Gaga, Mick Jagger, Keith Richards, Phil Everly, Don Everly, Cab Calloway, and Sarah Vaughn?

That would seem to be a Herculean task. But actually, it's quite simple.

Note that we can determine how many duets we have with Elton, Lady Gaga, and Tony with the simple formula:

... and we get the right answer.

So with the group of ten performers we can look at the corresponding formula:

... which is a lot of duets.

But what if you want a duet where the musicians and singers are Elton, Tony, Lady Gaga, Mick, Keith, Phil, Don, Cab, Sarah, the Isley Brothers, the Andrews Sisters, and the 1958 New York Philharmonic (including the conductor)?

Well, as anyone can determine the number is 1,506,330,009,228,829,772,404,988,538,763,529,846,162,082,459,336,810,899,526,673,450,298,333,603,809,240,404,533,930,346,048,856,880,992,304,889,972,886,391,982,781,925,516,650,386,163,148,886,543,925,934,991,250,135,330,895,622,061,298,810,880,000,000,000,000,000,000,000,000,000,000.

Of course, the calculation will be left as an exercise for the reader.

A Lot of Duets

References and Further Reading

"Tony Bennett and Lady Gaga's Newest Collaboration to Debut This Fall," CNN, September 15, 2021.