A) \[{{8.}^{6}}{{C}_{4}}{{.}^{7}}{{C}_{4}}\]
B) \[{{6.7.}^{8}}{{C}_{4}}\]
C) \[{{6.8.}^{7}}{{C}_{4}}.\]
D) \[{{7.}^{6}}{{C}_{4}}{{.}^{8}}{{C}_{4}}\]
Correct Answer: D
Solution :
[d] First let us arrange M, I, I, I, I, P, P Which can be done in \[\frac{7!}{4!2!}\] ways Now 4 S can be kept at any of the ticked places in \[^{8}{{C}_{4}}\] ways so that no two S are adjacent. Total required ways \[={{\frac{7!}{4!2!}}^{8}}{{C}_{4}}={{\frac{7!}{4!2!}}^{8}}{{C}_{4}}=7\times {{\,}^{6}}{{C}_{4}}\times {{\,}^{8}}{{C}_{4}}\]
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