Match the four counting results. Column I: (A) Dictionary rank of SUCCESS among arrangements of its letters. (B) A factor P of 10000000099 lies between 9000 and 10000: sum of its digits. (C) Number of

Question

Match the four counting results. Column I: (A) Dictionary rank of SUCCESS among arrangements of its letters. (B) A factor $P$ of 10000000099 lies between 9000 and 10000: sum of its digits. (C) Number of trailing zeros in 83!. (D) Ordered three-strip flags formed using up to four identical yellow, three red, two pink strips. Column II: (p) 13 (q) 19 (r) 271 (s) 331 (t) 26

Column I	Column II
(A) Dictionary rank of SUCCESS among arrangements of its letters.	(p) 13
(B) A factor $P$ of 10000000099 lies between 9000 and 10000: sum of its digits.	(q) 19
(C) Number of trailing zeros in 83!.	(r) 271
(D) Ordered three-strip flags formed using up to four identical yellow, three red, two pink strips.	(s) 331
	(t) 26

TestHub · Accepted Answer

Ordering SUCCESS lexicographically with repeated letters gives rank 331. Since $(10 0^{2} - 100 + 1)$ divides $10 0^{5} +$ $100 - 1, P = 9901$ has digit sum 19. For C, $⌊ 83/5 ⌋ + ⌊ 83/25 ⌋ = 16 + 3 = 19$ . Of $3^{3} = 27$ color sequences for D, only PPP is impossible; thus 26 flags.

Note: option (t) corrected from the printed 20 to the true value 26.

Mathematics - Permutation & Combination Question with Solution | TestHub

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