Problem 1: Give two different examples of a 4-permutation of letters from ABCDEF
ID: 3706978 • Letter: P
Question
Problem 1: Give two different examples of a 4-permutation of letters from ABCDEFG. Give a formula for the number of 4-permutations of letters from ABCDEFG. Give two different examples of a selection (without repetition) of four letters from 1a. 1b. 1c. ABCDEFG Id. Give a formula for the number of selections (without repetition) of four letters from ABCDEFG Give two different examples of a selection (with repetition) of ten letters from ABCDEFG le. Give a formula for the number of selections (with repetition) of ten letters from ABCDEFG If. Give two different examples of an arrangement of the letters ABCDEFG with three A's and all the other letters appear once. 1g. Give a formula for the number of arrangements of the letters ABCDEFG with three A's and all the other letters appear once. 1h. Give two different examples of distributing seven identical oranges into boxes labeled A, B, C. li. Give a formula for the number of ways to distribute n identical oranges into boxes labeled A, B, C lj.Explanation / Answer
1a) 4-permutation of letters from ABCDEFG means out of 7 letters taken 4 at a time ie, CAGE, BADD
1b) Formula for 4-permutation of letters is C(n,r) = C(7,4)
1c) Selection (without repetition) of 4 letters from ABCDEFG is ABCD, CDEF
1d) Formula for selection (without repetition) of 4 letters from ABCDEFG is same as above since here the letters are not repeated ie, C(n,r) = C(7,4)
1e) Selection (with repetition) of 10 letters from ABCDEFG is ABBCCDDEFG, GGFEDBAACD