Partnership

Ham, Sam and Tam formed a partnership to run a petrol station. The partnership agreement expressly stated that the partnership business was to be limited exclusively to the sale of petrol.
In January 20X8 Sam received £10,000 from the partnership’s bank drawn on its overdraft facility. He told the bank that the money was to finance a short-term partnership debt but in fact he used the money to pay
for a round-the-world cruise. In February 20X8 Tam entered into a £15,000 contract on behalf of the partnership to buy a stock of bicycles, which he hoped to sell from the garage forecourt.
Explain whether Tam has acted within his authority?

Sir here in the above case,
a) Tam does not have express authority for buying and selling bicycles right?
b) But the 3rd party was not notified, right?
c) therefore, firm is not bound by implied authority of Tam, right?

Please answer me a,b and c separately in just yes or no.