Solveeit Logo
Login

Question

Question: \(34C_{5} + {\sum_{r = 0}^{4}}^{38 - r}C_{4}\) =...

34C5+∑r=0438−rC434C_{5} + {\sum_{r = 0}^{4}}^{38 - r}C_{4} =

A

38C538C_{5}

B

39C5

C

34C434C_{4}

D

34C434C_{4}

Answer

39C5

Explanation

Solution

Sol. = 34C5+38C4+37C4+36C4+35C4+34C4\mathbf{34}\mathbf{C}_{\mathbf{5}}\mathbf{+}^{\mathbf{38}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{37}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{36}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{35}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{34}}\mathbf{C}_{\mathbf{4}}

= 38C4+37C4+36C4+35C4+35C5\mathbf{38}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{37}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{36}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{35}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{35}}\mathbf{C}_{\mathbf{5}}

= 38C4+37C4+36C4+36C5=38C4+37C4+37C5\mathbf{38}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{37}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{36}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{36}}\mathbf{C}_{\mathbf{5}}\mathbf{=}^{\mathbf{38}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{37}}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{37}}\mathbf{C}_{\mathbf{5}}

= 38C4+38C5=39C5\mathbf{38}\mathbf{C}_{\mathbf{4}}\mathbf{+}^{\mathbf{38}}\mathbf{C}_{\mathbf{5}}\mathbf{=}^{\mathbf{39}}\mathbf{C}_{\mathbf{5}}.