Question

In How many ways 100 blankets can be distributed to 6 beggars if each get odd number of blankets.

Answer 1

\((2m_1 + 1)+ (2m_2 + 1) + (2m_3 + 1)+ (2m_4+1)+(2m_5 + 1) + (2m_6 + 1) \\= 100 \,m_1, m_2,m_3,m_4,m_5,m_6\ge0\)

⇒ \(2(m_1 + m_2 + m_3 + m_4+ m_5 + m_6) = 100- 6 = 94\)

⇒ \(m_1 + m_2 + m_3 + m_4+m_5 + m_6= \frac{94}2=47\)

\(n = 47, r =6\)

Total no. of ways = \(^{n+ r - 1}C_{r - 1}\)

\(=\, ^{47 +6-1}C_{6 - 1}\)

\(=\,^{52}C_5\)