Suppose we want to choose six letters without replacement from nine distinct letters if the order of the choices is not taken into consideration how many ways can this be done
If the order of the choices is not taken into consideration, then we are looking at choosing six letters out of nine distinct letters. This can be solved using combinations.
The number of ways to choose six letters out of nine distinct letters can be found using the formula for combinations, which is given by:
C(n, r) = n! / [(n - r)! * r!]
where n is the total number of items to choose from, and r is the number of items to choose.
In this case, n = 9 (nine distinct letters) and r = 6 (six letters to choose).
Thus, the number of ways to choose six letters without replacement from nine distinct letters is:
C(9, 6) = 9! / [(9 - 6)! * 6!]
= 9! / (3! * 6!)
= (9 * 8 * 7 * 6 * 5 * 4) / (3 * 2 * 1)
= 84
Therefore, there are 84 ways to choose six letters without replacement from nine distinct letters if the order of the choices is not taken into consideration.
To find the number of ways to choose six letters without replacement from nine distinct letters, we can use the combination formula.
The combination formula is given by:
C(n, r) = n! / (r! * (n - r)!)
Where n is the total number of items, and r is the number of items being chosen without replacement.
In this case, we have nine distinct letters and want to choose six of them without replacement. Using the combination formula:
C(9, 6) = 9! / (6! * (9 - 6)!)
= (9 * 8 * 7 * 6 * 5 * 4) / (6 * 5 * 4 * 3 * 2 * 1)
= 84
Therefore, there are 84 ways to choose six letters without replacement from nine distinct letters, considering the order of the choices is not taken into consideration.