Step by step workout

step 1

Formula:

nPr =n!  / (n1! n2! . . . nk!)

. Input Parameters & Values:

Total number of alphabets (n) & subsets (n1, n2, . . nk) in the word "SINOGEN"

• n = 7
• Subsets : S = 1; I = 1; N = 2; O = 1; G = 1; E = 1;
• n1(S) = 1, n2(I) = 1, n3(N) = 2, n4(O) = 1, n5(G) = 1, n6(E) = 1

step 2

nPr formula

= 7!  / (1! 1! 2! 1! 1! 1! )

= 1 x 2 x 3 x 4 x 5 x 6 x 7  / {(1) (1) (1 x 2) (1) (1) (1)}

= 5040  / 2

= 2520

In 2520 distinct ways, the letters of word "SINOGEN" can be arranged.

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SIEGNNO SIEGNON SIEGONN SIENGNO SIENGON SIENNGO SIENNOG SIENOGN SIENONG SIEOGNN SIEONGN SIEONNG SIGENNO SIGENON SIGEONN SIGNENO SIGNEON SIGNNEO SIGNNOE SIGNOEN SIGNONE SIGOENN SIGONEN SIGONNE SINEGNO SINEGON SINENGO SINENOG SINEOGN SINEONG SINGENO SINGEON SINGNEO SINGNOE SINGOEN SINGONE SINNEGO SINNEOG SINNGEO SINNGOE SINNOEG SINNOGE SINOEGN SINOENG SINOGEN SINOGNE SINONEG SINONGE SIOEGNN SIOENGN SIOENNG SIOGENN SIOGNEN SIOGNNE SIONEGN SIONENG SIONGEN SIONGNE SIONNEG SIONNGE SNEGINO SNEGION SNEGNIO SNEGNOI SNEGOIN SNEGONI SNEIGNO SNEIGON SNEINGO SNEINOG

.......(2520)