can you help me with this problem:
This problem concerns lists made from the letters A,B,C,D,E,F,G,H,I,J.
(a) How many length-5 lists can be made from these letters if repetition is not
allowed and the list must begin with a vowel?
(b) How many length-5 lists can be made from these letters if repetition is not
allowed and the list must begin and end with a vowel?
(c) How many length-5 lists can be made from these letters if repetition is not
allowed and the list must contain exactly one A?
for a) I said :
3*9*8*7*6
for b)
I did
3*8*7*6*2
for c) I did
5*(9*8*7*6*1)
I am not sure of a or b
Help is appreciated!
Best Answer
Yes. That looks right.
Select one of three vowels for first place, then select and arrange four of nine remaining letters for the others. $${^{3}\mathrm P_{1}}\;{^{9}\mathrm P_{4}} = 3\cdot 9\cdot 8\cdot 7\cdot 6$$
Select and arrange two of three vowels for first and last place, then do so for three of eight letters in the middle three places. $${^{3}\mathrm P_{2}}\,{^{8}\mathrm P_{3}} = 3\cdot 2\cdot 8\cdot 7\cdot 6$$
Select a place to contain the
A, then select and permute four of nine letters. $${^{5}\mathrm C_{1}} \;{^{9}\mathrm P_{4}} = 5\cdot 9\cdot 8\cdot 7\cdot 6$$