Question

suppose we want to choose 6 letters without replacement from 13 distinct letters. A) how many ways can this be done if order does not matter? B) how many ways can this be done if order of choices matters

Answer 1

Answer: A) 1716   B) 1235520

Step-by-step explanation:

• If order doesn't matter , then we use combinations, where the number of combinations of selecting r things from n is given by :-

$^nC_r=\dfrac{n!}{r!(n-r)!}$

• If order matters , then we use permutations, where the number of permutations of selecting r things from n is given by :-

$^nP_r=\dfrac{n!}{(n-r)!}$

Given, Total distinct letters = 13

To choose = 6 letters

A) Number of ways to choose (if order does not matter)=$^{13}C_6$

$=\dfrac{13!}{6!7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!}{(720)\times 7!}\\\\= 1716$

B) Number of ways to choose (if order matters)=$^{13}P_6$

$=\dfrac{13!}{7!}=\dfrac{13\times12\times11\times10\times9\times8\times7!} 7!}\\\\= 1235520$

Hence, A) 1716   B) 1235520