The work environment at McFinsey is rather competitive. After $4$ years of working as an

associate, a consultant goes $$either up or out$,$ i$.$e$.$ becomes a manager or is dismissed from

the company. Similarly, after $6$ years a manager either becomes a partner or is dismissed.

The company recruits MBAs as associate consultants, no hires are made at the manager or

partner level. A partner stays with the company for another $10$ years $($total of $20$ years with

the company$).$

$($a$)$ How many new MBA graduates does McFinsey have to hire every year?

$($b$)$ What are the odds that a new hire at McFinsey will become partner $($as opposed to

being dismissed after $4$ years or $10$ years$)?$