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HH'\") The number of all ternary strings with exactly i 0's, exactly j 1's and exactly k 2's is denoted by ( I J k i+5l+k). (Your formula should be in terms of factorials or binomial coefcients. (a) Find a formula for ( I j k Please explain your work.) (b) Give a combinatorial argument for the identity: i+j+k _ i+j+k1 + i+j+k1 + i+j+k1 7:13.316 i_17j1k i1j_11k i7j2k_1 (c) Use this recurrence to design a ranking algorithm for the set of all ternary strings with exactly 2' zeros, j ones, and k twos. (d) Rank 1002121, 2111020, 0110221 using your ranking algorithm from the previous step. (you can Show your work by writing out each term of your calculation for each string.)