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# Number Theory/Factorial question.

Question
I am trying to figure out the equation for this situation. It is a modified factorial. You have 5 buttons. Each button can be pressed individually or in combination with other buttons. Your button press sequences can range from 1 individual or combination button press to five individual or combination button presses so long as any one button is pressed only one time.  How many different combinations can you generate?

Hello bart
You have used the word combination, which means you are not interested in the order that the buttons are pressed.  Only in the final result.  In this case each button can be pressed or not pressed.  2 possibilities for each, so that makes 2^5 = 32 ways.  But I think my understanding is that you must have at least one button pressed, making 31 ways.
If instead you want the number of permutations, so the order of pressing is important, there would be 5 ways for 1 button, 5*4 ways for 2 buttons, 5*4*3 ways for 3, 5*4*3*2 for 4 and 5*4*3*2*1 for 5.  That makes 325.
Regards
vijilant

Number Theory

Volunteer

#### Vijilant

##### Expertise

Most questions on number theory, divisibility, primes, Euclidean algorithm, Fermat`s theorem, Wilson`s theorem, factorisation, euclidean algorithm, diophantine equations, Chinese remainder theorem, group theory, congruences, continued fractions.

##### Experience

Teacher of math for 53 years

Organizations
AQA Doncaster Bridge Club Danum Strings Orchestra Doncaster Conservative Club Danum Strings Orchestra Simply Voices Choir Doncaster TNS mystery shopping St Paul's Music Group Cantley

Publications
Journal of mathematics and its applications M500 magazine

Education/Credentials
BSc (Hons) Liverpool (Science). BA (Hons) OU (Mathematics)

Awards and Honors
State Scholarship 1955 Highest Score in Yorkshire on OU course MST209 £50 prize First class honours in OU BA Mathematics

Past/Present Clients
I taught John Birt, former Director of the BBC in 1961. His homework book was the most perfect I have ever marked. And also the most neat. I could tell he was destined for great things. One of my classmates was the poet Roger McGough, and I have a mention in his autobiography.