Question

The letters of the word ${}^{\prime }KUBE{R}^{\prime }$ are written in all possible orders and arranged in a dictionary order. Find the rank of the word ${}^{\prime }KUBE{R}^{\prime }$.

• A. $67$
• B. $68$
• C. $65$
• D. $69$

Answer 1

The correct option is A $67$

Given word $KUBER$

Alphabetical order $BEKRU$

Number of words begning with $B⟶4!=24$

Number of words begning with $E⟶4!=24$

Number of words begning with $KB⟶3!=6$

Number of words begning with $KE⟶3!=6$

Number of words begning with $KR⟶3!=6$

Number of words begning with $KUBER⟶0!=1$

Total $=67$

Rank of $KUBER=67$