An ordinary cubical dice having six faces markedwith alphabets A, B, C, D, E, and F is thrown `n`times andht list of `n`alphabets showing p are noted. Find the total number ofways in which among the alphabets A, B, C D, E and F only three of themappear in the list.

An ordinary cubical dice having six faces markedwith alphabets A, B, C

1.	An ordinary cubical dice having six faces markedwith alphabets A, B, C, D, E, and F is thrown `n`times andht list of `n`alphabets showing p are noted. Find the total number ofways in which among the alphabets A, B, C D, E and F only three of themappear in the list.
Answer» Three letters from six letters can be selected in `""^(6)C_(3)` ways. Consider one such set of letters {A,B,C}. Now, if each throw of dice shows either letter A, B or C then number of cases is `3^(n)`. But this includes those cases also in which exactly one letter or exactly two letters from A, B and C appear. Number of cases in which exactly one letter appears in all throws is 3. Number of cases in which exactly two letters appear (each at least once) is `""^(3)C_(2)(2^(n)-2)`. So, required number of cases `=""^(6)C_(3)xx[3^(n)- ""^(3)C_(2)(2^(n)-2)-3]`

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An ordinary cubical dice having six faces markedwith alphabets A, B, C, D, E, and F is thrown `n`times andht list of `n`alphabets showing p are noted. Find the total number ofways in which among the alphabets A, B, C D, E and F only three of themappear in the list.

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