A man has 3 friends. If is number of ways he can invite one friend everyday for dinner on 6 successive nights so that no friend is invited more than 3 times then the value of is |

A man has 3 friends. If is number of ways he can invite one friend everyday for dinner on 6 successive nights so that no friend is invited more than 3 times then the value of is |

1 Answer

127 votes

1. He can invite 2 friends three times each Lets select first those 2 friends in ways Now these two friends each three time can be invited on 6 days in Thus total number of ways 2 friends can be invited three times 2. Another possibility is that he invites all three friends 2 times each Then number of ways 3. One more possibility is that he invites one friend three times, one two times and one three times Then number of ways Hence total number of ways |

127 votes

127